<PAGE>   1
                                                                  EXHIBIT 10.9.2

THIS WARRANT AND ANY SHARES ACQUIRED UPON EXERCISE OF THIS WARRANT HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE
SECURITIES LAWS AND MAY NOT BE SOLD OR TRANSFERRED WITHOUT COMPLIANCE WITH THE
REGISTRATION OR QUALIFICATION PROVISIONS OF APPLICABLE FEDERAL AND STATE
SECURITIES LAWS OR APPLICABLE EXEMPTIONS THEREFROM.

THE SECURITIES REPRESENTED BY THIS WARRANT ARE SUBJECT TO A SECOND AMENDED AND
RESTATED STOCKHOLDERS' AGREEMENT DATED AS OF JUNE 30, 1998 (THE "STOCKHOLDERS'
AGREEMENT"). THE TRANSFERABILITY OF THESE SECURITIES IS RESTRICTED, AND THE
SECURITIES MAY NOT BE SOLD OR OTHERWISE TRANSFERRED EXCEPT PURSUANT TO THE TERMS
AND CONDITIONS OF THE STOCKHOLDERS' AGREEMENT. THE SECURITIES REPRESENTED BY
THIS WARRANT ARE ALSO SUBJECT TO A SECOND AMENDED AND RESTATED REGISTRATION
RIGHTS AGREEMENT DATED AS OF JUNE 30, 1998 (THE "REGISTRATION AGREEMENT").
COPIES OF THE STOCKHOLDERS' AGREEMENT AND THE REGISTRATION AGREEMENT ARE ON FILE
AT THE OFFICE OF THE SECRETARY OF THE COMPANY.

No. ___                                   Right to Purchase __________ Shares of
                                                           Common Stock of
                                                  Odyssey HealthCare, Inc.

                            ODYSSEY HEALTHCARE, INC.

                          COMMON STOCK PURCHASE WARRANT

                                                                  July ___, 1998

         Odyssey HealthCare, Inc., a Delaware corporation (the "Company"),
hereby certifies that, for value received,________________. or assigns, is
entitled, subject to the terms set forth below, to purchase from the Company at
any time or from time to time before 5:00 p.m., Boston time, on March 31, 2005,
or such later time as may be specified in Section 17 hereof, _________ fully
paid and nonassessable shares of Common Stock, par value $0.001 per share, of
the Company, at a purchase price per share of $0.01 (such purchase price per
share as adjusted from time to time as herein provided is referred to herein as
the "Purchase Price"). The number and character of such shares of Common Stock
and the Purchase Price are subject to adjustment as provided herein.

         This Warrant evidences the right to purchase shares of Common Stock of
the Company issued pursuant to a certain Senior Subordinated Note and Warrant
Purchase Agreement (the "Agreement"), dated as of June 30, 1998 by and among the
Company, HNT Hospice of North Texas, a Texas corporation, Odyssey HealthCare of
Birmingham, Inc., a Delaware corporation, Odyssey HealthCare of Central Indiana,
Inc., a Delaware corporation, Odyssey HealthCare of


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                                      -2-


Detroit, a Delaware corporation, Odyssey HealthCare of Phoenix, a Delaware
corporation, Odyssey HealthCare of Milwaukee, Inc., a Delaware corporation,
Odyssey HealthCare of Central Texas, a Delaware corporation, Odyssey HealthCare
of Minneapolis, Inc., a Delaware corporation, Odyssey HealthCare of New Orleans,
a Delaware corporation, Odyssey HealthCare of Las Vegas, Inc., a Delaware
corporation, Odyssey HealthCare of Pennsylvania, Inc., a Delaware corporation,
Odyssey HealthCare of North Texas, Inc., a Delaware corporation, Odyssey
HealthCare of Houston, Inc., a Delaware corporation, Odyssey HealthCare of New
Jersey, Inc., a Delaware Corporation, and Odyssey HealthCare of Georgia, Inc., a
Delaware corporation, Capital Resource Lenders III, L.P., a Delaware limited
partnership, and CRP Investment Partners III, L.L.C., a Delaware limited
liability company, and subject to the Stockholders' Agreement and the
Registration Agreement, copies of which agreements are on file at the principal
office of the Company, and the holder of this Warrant shall be entitled to all
of the benefits and bound by all of the applicable obligations of the Agreement,
the Stockholders' Agreement and the Registration Agreement, as provided therein.

         As used herein the following terms, unless the context otherwise
requires, have the following respective meanings:

                  (a) The term "Company" shall include Odyssey HealthCare, Inc.
         and any corporation which shall succeed to, or assume the obligations
         of, the Company hereunder.

                  (b) The term "Common Stock" includes (i) the Company's Common
         Stock, par value $0.001 per share, as authorized on the date of the
         Agreement, (ii) any other capital stock of any class or classes
         (however designated) of the Company, authorized on or after such date,
         the holders of which shall have the right, without limitation as to
         amount per share, either to all or to a share of the balance of current
         dividends and liquidating distributions after the payment of dividends
         and distributions on any shares entitled to preference in the payment
         thereof, and the holders of which shall ordinarily, in the absence of
         contingencies, be entitled to vote for the election of a majority of
         directors of the Company (even though the right so to vote may have
         been suspended by the happening of such a contingency) and (iii) any
         other securities into which or for which any of the securities
         described in (i) or (ii) above may be converted or exchanged pursuant
         to a plan of recapitalization, reorganization, merger, sale of assets
         or otherwise.

                  (c) The term "Conversion Price" means the amount that the
         Purchase Price would be, immediately prior to the determination of the
         Conversion Price and giving effect to all adjustments that would have
         been required under Section 5, if the initial Purchase Price had been
         $1.75 per share of Common Stock.

                  (d) The term "Other Securities" refers to any stock (other
         than Common Stock) and other securities of the Company or any other
         person (corporate or otherwise) which the holders of the Warrants at
         any time shall be entitled to receive, or shall have received, on the
         exercise of the Warrants, in lieu of or in addition to Common Stock, or
         which at any time shall be issuable or shall have been issued in
         exchange for or in replacement of Common Stock or Other Securities
         pursuant to Section 0 or otherwise.



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                                      -3-


         Exercise of Warrant.

                  Full Exercise. This Warrant may be exercised at any time
before its expiration in full by the holder hereof by surrender of this Warrant,
with the form of subscription at the end hereof duly executed by such holder, to
the Company at its principal office, accompanied by payment, in cash or by
certified or official bank check payable to the order of the Company, in the
amount obtained by multiplying the number of shares of Common Stock for which
this Warrant is then exercisable by the Purchase Price then in effect.

                  Partial Exercise. This Warrant may be exercised at any time
before its expiration in part (in lots of 100 shares or, if this Warrant is then
exercisable for a lesser amount, in such lesser amount) by surrender of this
Warrant and payment of the Purchase Price then in effect in the manner and at
the place provided in subsection 1.1, except that the amount payable by the
holder on such partial exercise shall be the amount obtained by multiplying (a)
the number of shares of Common Stock designated by the holder in the form of
subscription at the end hereof by (b) the Purchase Price then in effect. On any
such partial exercise the Company at its expense will forthwith issue and
deliver to or upon the order of the holder hereof a new Warrant or Warrants of
like tenor, in the name of the holder hereof or as such holder (upon payment by
such holder of any applicable transfer taxes) may request, calling in the
aggregate on the face or faces thereof for the number of shares of Common Stock
for which such Warrant or Warrants may still be exercised.

                  Payment by Surrender of Notes. Notwithstanding the payment
provisions of subsections 1.1 and 1.2, all or part of the payment due upon
exercise of this Warrant in full or in part may be made by the surrender by such
holder to the Company of any of the Company's Notes issued pursuant to the
Agreement and such Notes so surrendered shall be credited against such payment
in an amount equal to the principal amount thereof plus premium (if any) and
accrued interest to the date of surrender.

                  Company Acknowledgment. The Company will, at the time of the
exercise of this Warrant, upon the request of the holder hereof acknowledge in
writing its continuing obligation to afford to such holder any rights to which
such holder shall continue to be entitled after such exercise in accordance with
the provisions of this Warrant. If the holder shall fail to make any such
request, such failure shall not affect the continuing obligation of the Company
to afford to such holder any such rights.

                  Trustee for Warrant Holders. In the event that a bank or trust
company shall have been appointed as trustee for the holders of the Warrants
pursuant to subsection 4.2, such bank or trust company shall have all the powers
and duties of a warrant agent appointed pursuant to Section 12 and shall accept,
in its own name for the account of the Company or such successor person as may
be entitled thereto, all amounts otherwise payable to the Company or such
successor, as the case may be, on exercise of this Warrant pursuant to this
Section 1.

                  Net Issue Election. The holder may elect to receive, without
the payment by the holder of any additional consideration, shares equal to the
value of this Warrant or any portion



<PAGE>   4
                                      -4-


hereof by the surrender of this Warrant or such portion to the Company, with the
net issue election notice annexed hereto duly executed, at the office of the
Company. Thereupon, the Company shall issue to the holder such number of fully
paid and nonassessable shares of Common Stock as is computed using the following
formula:

                           X   =   Y (A-B)
                                   -------
                                      A

where    X =      the number of shares to be issued to the holder pursuant to
                  this Section 1.6.

         Y =      the number of shares covered by this Warrant in respect of
                  which the net issue election is made pursuant to this Section
                  1.6.

         A =      the fair market value of one share of Common Stock, as
                  determined in accordance with the provisions of this Section
                  1.6.

         B =      the Purchase Price in effect under this Warrant at the time
                  the net issue election is made pursuant to this Section 1.6.

For purposes of this Section 1.6, the "fair market value" per share of the
Company's Common Stock shall mean:

                  If the net issue election is exercised in connection with and
         contingent upon the Company's initial public offering, and if the
         Company's registration statement relating to such offering has been
         declared effective by the Securities and Exchange Commission, then the
         initial "Price to Public" specified in the final prospectus with
         respect to such offering; or

                  If the net issue election is not exercised in connection with
         and contingent upon the Company's initial public offering, then as
         follows:

                           If the Common Stock is traded on a national
                                    securities exchange or admitted to unlisted
                                    trading privileges on such an exchange, or
                                    is listed on the National Market (the
                                    "National Market") of the National
                                    Association of Securities Dealers Automated
                                    Quotations System (the "NASDAQ"), the fair
                                    market value shall be the average of the
                                    last reported sale prices of the Common
                                    Stock on such exchange or on the National
                                    Market over the ten (10) consecutive
                                    Business Days immediately preceding the
                                    effective date of exercise of the net issue
                                    election or if the last reported sale price
                                    information is not available for such days,
                                    the average of the mean of the closing bid
                                    and asked prices for such day on such
                                    exchange or on the National Market;

                           If the Common Stock is not so listed or admitted to
                                    unlisted trading privileges, the fair market
                                    value shall be the average of the mean of



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                                      -5-


                                    the last bid and asked prices reported over
                                    the ten (10) consecutive Business Days
                                    immediately preceding the effective date of
                                    exercise of the net issue election (1) by
                                    the NASDAQ or (2) if reports are unavailable
                                    under clause (1) above, by the National
                                    Quotation Bureau Incorporated; and

                           If the Common Stock is not so listed or admitted to
                                    unlisted trading privileges and bid and ask
                                    prices are not reported, the fair market
                                    value shall be the price per share which the
                                    Company could obtain from a willing buyer
                                    for shares sold by the Company from
                                    authorized but unissued shares, as such
                                    price shall be determined by mutual
                                    agreement of the Company and the holder of
                                    this Warrant. If the holder of this Warrant
                                    and the Company are unable to agree on such
                                    fair market value, the fair market value
                                    shall be determined in good faith by the
                                    Board of Directors of the Company.

         Delivery of Stock Certificates, etc. on Exercise. As soon as
practicable after the exercise of this Warrant in full or in part, and in any
event within ten (10) days thereafter, the Company at its expense (including the
payment by it of any applicable issue taxes) will cause to be issued in the name
of and delivered to the holder hereof, or as such holder (upon payment by such
holder of any applicable transfer taxes) may direct, a certificate or
certificates for the number of fully paid and nonassessable shares of Common
Stock (or Other Securities) to which such holder shall be entitled on such
exercise, plus, in lieu of any fractional share to which such holder would
otherwise be entitled, cash equal to such fraction multiplied by the then
current market value of one full share, together with any other stock or other
securities and property (including cash, where applicable) to which such holder
is entitled upon such exercise pursuant to Section 1 or otherwise.

         Adjustment for Dividends in Other Stock, Property, etc.;
Reclassification, etc. In case at any time or from time to time, the holders of
Common Stock (or Other Securities) in their capacity as such shall have
received, or (on or after the record date fixed for the determination of
shareholders eligible to receive) shall have become entitled to receive, without
payment therefor,

                  other or additional stock or other securities or property
         (other than cash) by way of dividend, or

                  any cash (excluding cash dividends payable solely out of
         earnings or earned surplus of the Company), or

                  other or additional stock or other securities or property
         (including cash) by way of spin-off, split-up, reclassification,
         recapitalization, combination of shares or similar corporate
         rearrangement,

other than additional shares of Common Stock (or Other Securities) issued as a
stock dividend or in a stock-split (adjustments in respect of which are provided
for in Section 5), then and in each



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                                      -6-


such case the holder of this Warrant, on the exercise hereof as provided in
Section 1, shall be entitled to receive the amount of stock and other securities
and property (including cash in the cases referred to in subdivisions (b) and
(c) of this Section 3) which such holder would hold on the date of such exercise
if on the date hereof he had been the holder of record of the number of shares
of Common Stock called for on the face of this Warrant and had thereafter,
during the period from the date hereof to and including the date of such
exercise, retained such shares and all such other or additional stock and other
securities and property (including cash in the cases referred to in subdivisions
(b) and (c) of this Section 3) receivable by him as aforesaid during such
period, giving effect to all adjustments called for during such period by
Sections 4 and 5.

         Adjustment for Reorganization, Consolidation, Merger, etc.

                  Reorganization, Consolidation, Merger, etc. In case at any
time or from time to time, the Company shall (a) effect a reorganization, (b)
consolidate with or merge into any other Person, or (c) transfer all or
substantially all of its properties or assets to any other Person under any plan
or arrangement contemplating the dissolution of the Company, then, in each such
case, the holder of this Warrant, on the exercise hereof as provided in Section
1 at any time after the consummation of such reorganization, consolidation or
merger or the effective date of such dissolution, as the case may be, shall
receive, in lieu of the Common Stock (or Other Securities) issuable on such
exercise prior to such consummation or such effective date, the stock and other
securities and property (including cash) to which such holder would have been
entitled upon such consummation or in connection with such dissolution, as the
case may be, if such holder had so exercised this Warrant, immediately prior
thereto, all subject to further adjustment thereafter as provided in Sections 3
and 5.

                  Dissolution. In the event of any dissolution of the Company
following the transfer of all or substantially all of its properties or assets,
the Company, prior to such dissolution, shall at its expense deliver or cause to
be delivered the stock and other securities and property (including cash, where
applicable) receivable by the holders of the Warrants after the effective date
of such dissolution pursuant to this Section 4 to a bank or trust company having
its principal office in Boston, Massachusetts, as trustee for the holder or
holders of the Warrants.

                  Continuation of Terms. Upon any reorganization, consolidation,
merger or transfer (and any dissolution following any transfer) referred to in
this Section 4, this Warrant shall continue in full force and effect, subject to
expiration in accordance with Section 17 hereof, and the terms hereof shall be
applicable to the shares of stock and other securities and property receivable
on the exercise of this Warrant after the consummation of such reorganization,
consolidation or merger or the effective date of dissolution following any such
transfer, as the case may be, and shall be binding upon the issuer of any such
stock or other securities, including, in the case of any such transfer, the
person acquiring all or substantially all of the properties or assets of the
Company, whether or not such person shall have expressly assumed the terms of
this Warrant as provided in Section 6.



<PAGE>   7
                                      -7-


         Anti-Dilution Adjustment.

                  General. The Purchase Price shall be subject to adjustment
from time to time as hereinafter provided. Upon each adjustment of the Purchase
Price, the holder of this Warrant shall thereafter be entitled to purchase, at
the Purchase Price resulting from such adjustment, the number of shares obtained
by multiplying the Purchase Price in effect immediately prior to such adjustment
by the number of shares purchasable pursuant hereto immediately prior to such
adjustment and dividing the product thereof by the Purchase Price resulting from
such adjustment.

                  Purchase Price Adjustments. If and whenever after the date
hereof the Company shall issue or sell any shares of its Common Stock (except
(i) upon exercise of this Warrant, (ii) upon conversion of the Preferred Stock
(as defined in the Agreement) outstanding on the date hereof, (iii) upon
exercise of options or other rights to purchase up to an aggregate of 2,278,000
shares of Common Stock issued or to be issued to employees, officers or
directors of, or consultants or advisors to the Company pursuant to stock option
plans or other arrangements that are approved by the Board of Directors of the
Company, (iv) upon exercise of the warrants (the "Preferred Warrants") issued
pursuant to that certain Promissory Note and Warrant Purchase Agreement dated as
of May 22, 1998 among the Company and certain purchasers named therein, and (v)
upon conversion of the Series B Preferred Stock, $0.001 par value per share, of
the Company issuable upon exercise of the Preferred Warrants) for a
consideration per share less than the Purchase Price in effect immediately prior
to the time of such issue or sale, and/or the Company shall issue or sell any
shares of its Common Stock for a consideration per share less than the
Conversion Price on the date of such issue or sale, or shall be deemed under the
provisions of this Section 5 to have effected any such issuance or sale, then,
forthwith upon such issue or sale, the Purchase Price shall be reduced to the
price (calculated to the nearest $0.0001) obtained by multiplying the Purchase
Price in effect immediately prior to the time of such issue or sale by a
fraction, the numerator of which shall be the sum of (i) the number of shares of
Common Stock outstanding immediately prior to such issue or sale multiplied by
the Conversion Price immediately prior to such issue or sale plus (ii) the
consideration received by the Company upon such issue or sale, and the
denominator of which shall be the product of (iii) the total number of shares of
Common Stock outstanding immediately after such issue or sale, multiplied by
(iv) the Conversion Price immediately prior to such issue or sale.
Notwithstanding the foregoing, no adjustment of the Purchase Price shall be made
in an amount less than $0.0001 per share, but any such lesser adjustment shall
be carried forward and shall be made at the time of and together with the next
subsequent adjustment which together with any adjustments so carried forward
shall amount to $0.0001 per share or more.

                  Option Grants. In the event that at any time the Company shall
in any manner grant (directly, by assumption in a merger or otherwise) any
rights to subscribe for or to purchase, or any options for the purchase of,
Common Stock or any stock or securities convertible into or exchangeable for
Common Stock (except options or other rights to purchase up to an aggregate of
2,278,000 shares of Common Stock issued or to be issued to employees, officers
or directors of, or consultants or advisors to the Company pursuant to stock
option plans or other arrangements that are approved by the Board of Directors
of the Company) (such rights or options being herein called "Options" and such
convertible or exchangeable stock or securities being herein called "Convertible
Securities"), whether or not such Options or the right to convert or exchange
any such Convertible Securities are immediately exercisable, and the price per
share


<PAGE>   8
                                      -8-


for which Common Stock is issuable upon the exercise of such Options or upon
conversion or exchange of such Convertible Securities (determined by dividing
(i) the total amount, if any, received or receivable by the Company as
consideration for the granting of such Options, plus the minimum aggregate
amount of additional consideration payable to the Company upon the exercise of
all such Options, plus, in the case of any such Options which relate to
Convertible Securities, the minimum aggregate amount of additional
consideration, if any, payable upon the issue or sale of such Convertible
Securities and upon the conversion or exchange thereof, by (ii) the total number
of shares of Common Stock issuable upon the exercise of such Options or upon the
conversion or exchange of all such Convertible Securities issuable upon the
exercise of such Options) shall be less than the Purchase Price or the
Conversion Price in effect immediately prior to the time of the granting of such
Options, then the total number of shares of Common Stock issuable upon the
exercise of such Options or upon conversion or exchange of the total amount of
such Convertible Securities issuable upon the exercise of such Options shall (as
of the date of granting such Options) be deemed to be outstanding and to have
been issued for such price per share. Except as otherwise provided in subsection
5.5, no further adjustment of the Purchase Price shall be made upon the actual
issue of such Common Stock or of such Convertible Securities upon exercise of
such Options or upon the actual issue of such Common Stock upon conversion or
exchange of such Convertible Securities.

                  Convertible Security Grants. In the event that the Company
shall in any manner issue (directly, by assumption in a merger or otherwise) or
sell any Convertible Securities (other than pursuant to the exercise of Options
to purchase such Convertible Securities covered by subsection 5.3 or pursuant to
the exercise of the Preferred Warrants), whether or not the rights to exchange
or convert thereunder are immediately exercisable, and the price per share for
which Common Stock is issuable upon such conversion or exchange (determined by
dividing (i) the total amount received or receivable by the Company as
consideration for the issue or sale of such Convertible Securities, plus the
minimum aggregate amount of additional consideration, if any, payable to the
Company upon the conversion or exchange thereof, by (ii) the total maximum
number of shares of Common Stock issuable upon the conversion or exchange of all
such Convertible Securities) shall be less than the Purchase Price or the
Conversion Price in effect immediately prior to the time of such issue or sale,
then the total maximum number of shares of Common Stock issuable upon conversion
or exchange of all such Convertible Securities shall (as of the date of the
issue or sale of such Convertible Securities) be deemed to be outstanding and to
have been issued for such price per share, provided that, except as otherwise
provided in Section 5.5, no further adjustment of the Purchase Price shall be
made upon the actual issue of such Common Stock upon conversion or exchange of
such Convertible Securities.

                  Effect of Alteration to Option or Convertible Security Terms.
In connection with any change in, or the expiration or termination of, the
purchase rights under any Option or the conversion or exchange rights under any
Convertible Securities, the following provisions shall apply:

                  (A) If the purchase price provided for in any Option referred
         to in subsection 5.3, the additional consideration, if any, payable
         upon the conversion or exchange of any Convertible Securities referred
         to in subsection 5.3 or 5.4, or the rate at which any Convertible
         Securities referred to in subsection 5.3 or 5.4 are convertible into or



<PAGE>   9
                                      -9-


         exchangeable for Common Stock shall change at any time (other than
         under or by reason of provisions designed to protect against dilution),
         then the Purchase Price in effect at the time of such change shall
         forthwith be increased o decreased to the Purchase Price which would be
         in effect immediately after such change if (a) the adjustments which
         were made upon the issuance of such Options or Convertible Securities
         had been made upon the basis of (and taking into account the total
         consideration received for) (i) the issuance at that time of the Common
         Stock, if any, delivered upon the exercise of any such Options or upon
         the conversion or exchange of any such Convertible Securities before
         such change, and (ii) the issuance at that time of all such Options or
         Convertible Securities, with terms and provision reflecting such
         change, which are still outstanding after such change, and (b) the
         Purchase Price as adjusted pursuant to clause (a) preceding had been
         used as the basis for the adjustments required hereunder in connection
         with all other issues or sales of Common Stock, Options or Convertible
         Securities by the Company subsequent to the issuance of such Options or
         Convertible Securities.

                  (B) On the partial or complete expiration of any Options or
         termination of any right to convert or exchange Convertible Securities,
         the Purchase Price then in effect hereunder shall forthwith be
         increased or decreased to the Purchase Price which would be in effect
         at the time of such expiration or termination if (a) the adjustments
         which were made upon the issuance of such Options or Convertible
         Securities had been made upon the basis of (and taking into account the
         total consideration received for) (i) the issuance at that time of the
         Common Stock, if any, delivered upon the exercise of such Options or
         upon the conversion or exchange of such Convertible Securities before
         such expiration or termination, and (ii) the issuance at that time of
         only those such Options or Convertible Securities which remain
         outstanding after such expiration or termination, and (b) the Purchase
         Price as adjusted pursuant to clause (a) preceding had been used as the
         basis for adjustments required hereunder in connection with all other
         issues or sales of Common Stock, Options or Convertible Securities by
         the Company subsequent to the issuance of such Options or Convertible
         Securities.

                  (C) If the purchase price provided for in any Option referred
         to in subsection 5.3 or the rate at which any Convertible Securities
         referred to in subsection 5.3 or 5.4 are convertible into or
         exchangeable for Common Stock shall be reduced at any time under or by
         reason or provisions with respect thereto designed to protect against
         dilution, and the event causing such reduction is one that did not also
         require an adjustment in the Purchase Price under other provisions of
         this Section 5, then in case of the delivery of shares of Common Stock
         upon the exercise of any such Option or upon conversion or exchange of
         any such Convertible Securities, the Purchase Price then in effect
         hereunder shall forthwith be adjusted to such amount as would have
         obtained if such Option or Convertible Securities had never been issued
         and if the adjustments made upon the issuance of such Option or
         Convertible Securities had been made upon the basis of the issuance of
         (and taking into account the total consideration received for) the
         shares of Common Stock delivered as aforesaid (provided that the
         Conversion Price used in such determination shall be the Conversion
         Price on the date of issue of such shares); provided that no such
         adjustment shall be made unless the Purchase Price then in effect would
         be reduced thereby.



<PAGE>   10
                                      -10-


                  Dividends of Common Stock, Options or Convertible Securities.
In the event that the Company shall declare a dividend or make any other
distribution upon any stock of the Company payable in Common Stock, Options or
Convertible Securities, any Common Stock, Options or Convertible Securities, as
the case may be, issuable in payment of such dividend or distribution shall be
deemed to have been issued or sold without consideration.

                  Dilution in Case of Other Securities. In case any Other
Securities shall be issued or sold by the Company, or shall become subject to
issue upon the conversion or exchange of any stock (or Other Securities) of the
Company (or any other issuer of Other Securities or any other person referred to
in Section 4) or to subscription, purchase or other acquisition pursuant to any
rights or options granted by the Company (or such other issuer or person), for a
consideration per share such as to dilute the purchase rights evidenced by this
Warrant, the computations, adjustments and readjustments provided for in this
Section 5 with respect to the Purchase Price and the number of shares of Common
Stock issuable upon exercise of this Warrant shall be made as nearly as possible
in the manner so provided and applied to determine the amount of Other
Securities from time to time receivable on the exercise of the Warrants, so as
to protect the holders of the Warrants against the effect of such dilution.

                  Stock Splits and Reverse Splits. In the event that the Company
shall at any time subdivide its outstanding shares of Common Stock into a
greater number of shares, the Purchase Price in effect immediately prior to such
subdivision shall be proportionately reduced and the number of Warrant Shares
purchasable pursuant to this Warrant immediately prior to such subdivision shall
be proportionately increased, and conversely, in the event that the outstanding
shares of Common Stock of the Company shall at any time be combined into a
smaller number of shares, the Purchase Price in effect immediately prior to such
combination shall be proportionately increased and the number of Warrant Shares
purchasable upon the exercise of this Warrant immediately prior to such
combination shall be proportionately reduced. Except as provided in this
subsection 5.8 no adjustment in the Purchase Price and no change in the number
of Warrant Shares purchasable shall be made under this Section 5 as a result of
or by reason of any such subdivision or combination.

                  Determination of Consideration Received. For purposes of this
Section 5, the amount of consideration received by the Company in connection
with the issuance or sale of Common Stock, Options or Convertible Securities
shall be determined in accordance with the following:

                  (A) In the event that shares of Common Stock, Options or
         Convertible Securities shall be issued or sold for cash, the
         consideration received therefor shall be deemed to be the amount
         payable to the Company therefor.

                  (B) In the event that any shares of Common Stock, Options or
         Convertible Securities shall be issued or sold for a consideration
         other than cash, the amount of the consideration other than cash
         payable to the Company shall be deemed to be the fair value of such
         consideration as reasonably determined by the Board of Directors of the
         Company.



<PAGE>   11
                                      -11-


                  (C) The amount of consideration deemed to be received by the
         Company pursuant to the foregoing provisions of this subsection 5.9
         upon any issuance and/or sale, pursuant to an established compensation
         plan of the Company, to directors, officers or employees of the Company
         in connection with their employment, of shares of Common Stock, Options
         or Convertible Securities, shall be increased by the amount of any tax
         benefit realized by the Company as a result of such issuance and/or
         sale, the amount of such tax benefit being the amount by which the
         federal and/or state income or other tax liability of the Company shall
         be reduced by reason of any deduction or credit in respect of such
         issuance and/or sale.

                  (D) In the event that any shares of Common Stock, Options or
         Convertible Securities shall be issued in connection with any merger in
         which the Company is the surviving corporation, the amount of
         consideration therefor shall be deemed to be the fair value as
         reasonably determined by the Board of Directors of the Company of such
         portion of the assets and business of the nonsurviving corporation as
         such Board shall determine to be attributable to such Common Stock,
         Options or Convertible Securities, as the case may be.

                  (E) In the event that any Common Stock, Options and/or
         Convertible Securities shall be issued in connection with the issue and
         sale of other securities or property of the Company, together
         comprising one integral transaction in which no specific consideration
         is allocated to such Common Stock, Options or Convertible Securities by
         the parties thereto, such Common Stock, Options and/or Convertible
         Securities shall be deemed to have been issued without consideration.

                  Record Date as Date of Issue or Sale. In the event that at any
time the Company shall take a record of the holders of its Common Stock for the
purpose of entitling them (i) to receive a dividend or other distribution
payable in Common Stock, Options or Convertible Securities, or (ii) to subscribe
for or purchase Common Stock, Options or Convertible Securities, then such
record date shall be deemed to be the date of the issue or sale of the shares of
Common Stock deemed to have been issued or sold upon the declaration of such
dividend or the making of such other distribution or the date of the granting of
such right of subscription or purchase, as the case may be.

                  Treasury Stock. The number of shares of Common Stock
outstanding at any given time shall not include shares owned or held by or for
the account of the Company, and the disposition of any such shares (other than
their cancellation without reissuance) shall be considered an issue or sale of
Common Stock for the purposes of this Section 5.

         No Dilution or Impairment. The Company will not, by amendment of its
Articles of Incorporation or through any reorganization, transfer of assets,
consolidation, merger, dissolution, issue or sale of securities or any other
voluntary action, avoid or seek to avoid the observance or performance of any of
the terms of the Warrants, but will at all times in good faith assist in the
carrying out of all such terms and in the taking of all such action as may be
necessary or appropriate in order to protect the rights of the holders of the
Warrants against


<PAGE>   12
                                      -12-


dilution or other impairment. Without limiting the generality of the foregoing,
the Company (a) will not increase the par value or stated value of any shares of
stock receivable on the exercise of the Warrants above the amount payable
therefor on such exercise, (b) will take all such action as may be necessary or
appropriate in order that the Company may validly and legally issue fully paid
and nonassessable shares of stock on the exercise of all Warrants from time to
time outstanding, (c) will not issue any capital stock of any class which is
preferred as to dividends or as to the distribution of assets upon voluntary or
involuntary dissolution, liquidation or winding up, unless the rights of the
holders thereof shall be limited to a fixed sum or percentage of par value in
respect of participation in dividends and in any such distribution of assets,
and (d) will not transfer all or substantially all of its properties and assets
to any other person (corporate or otherwise), or consolidate with or merge into
any other person or permit any such person to consolidate with or merge into the
Company (if the Company is not the surviving person), unless such other person
shall expressly assume in writing and become bound by all the terms of the
Warrants.

         Accountants' Certificate as to Adjustments. In each case of any
adjustment or readjustment in the shares of Common Stock (or Other Securities)
issuable on the exercise of the Warrants, the Company at its expense will
promptly cause independent certified public accountants of recognized standing
selected by the Company to compute such adjustment or readjustment in accordance
with the terms of the Warrants and prepare a certificate setting forth such
adjustment or readjustment and showing in detail the facts upon which such
adjustment or readjustment is based, including a statement of (a) the
consideration received or receivable by the Company for any additional shares of
Common Stock (or Other Securities) issued or sold or deemed to have been issued
or sold, (b) the number of shares of Common Stock (or Other Securities)
outstanding or deemed to be outstanding, and (c) the Purchase Price and the
number of shares of Common Stock to be received upon exercise of this Warrant,
in effect immediately prior to such issue or sale and as adjusted and readjusted
as provided in this Warrant. The Company will forthwith mail a copy of each such
certificate to each holder of a Warrant, and will, on the written request at any
time of any holder of a Warrant, furnish to such holder a like certificate
setting forth the Purchase Price at the time in effect and showing how it was
calculated.

         Notices of Record Date, etc.  In the event of

                  any taking by the Company of a record of the holders of any
class of securities for the purpose of determining the holders thereof who are
entitled to receive any dividend or other distribution, or any right to
subscribe for, purchase or otherwise acquire any shares of stock of any class or
any other securities or property, or to receive any other right, or

                  any capital reorganization of the Company, any
reclassification or recapitalization of the capital stock of the Company or any
transfer of all or substantially all the assets of the Company to or
consolidation or merger of the Company with or into any other person, or any
voluntary or involuntary dissolution, liquidation or winding-up of the Company,
or

                  any proposed issue or grant by the Company of any shares of
stock of any class or any other securities, or any right or option to subscribe
for, purchase or otherwise acquire any


<PAGE>   13
                                      -13-


shares of stock of any class or any other securities (other than the issue of
Common Stock on the exercise of the Warrants),

then and in each such event the Company will mail or cause to be mailed to each
holder of a Warrant a notice specifying (i) the date on which any such record is
to be taken for the purpose of such dividend, distribution or right, and stating
the amount and character of such dividend, distribution or right, (ii) the date
on which any such reorganization, reclassification, recapitalization, transfer,
consolidation, merger, dissolution, liquidation or winding-up is to take place,
and the time, if any is to be fixed, as of which the holders of record of Common
Stock (or Other Securities) shall be entitled to exchange their shares of Common
Stock (or Other Securities) for securities or other property deliverable on such
reorganization, reclassification, recapitalization, transfer, consolidation,
merger, dissolution, liquidation or winding-up, and (iii) the amount and
character of any stock or other securities, or rights or options with respect
thereto, proposed to be issued or granted, the date of such proposed issue or
grant and the persons or class of persons to whom such proposed issue or grant
is to be offered or made. Such notice shall be mailed at least twenty (20) days
prior to the date specified in such notice on which any such action is to be
taken.

         Reservation of Stock, etc. Issuable on Exercise of Warrants. The
Company will at all times reserve and keep available, solely for issuance and
delivery on the exercise of the Warrants, all shares of Common Stock (or Other
Securities) from time to time issuable on the exercise of the Warrants.

         Exchange of Warrants. On surrender for exchange of any Warrant,
properly endorsed, to the Company, the Company at its expense will issue and
deliver to or on the order of the holder thereof a new Warrant or Warrants of
like tenor, in the name of such holder or as such holder (on payment by such
holder of any applicable transfer taxes) may direct, calling in the aggregate on
the face or faces thereof for the number of shares of Common Stock called for on
the face or faces of the Warrant or Warrants so surrendered.

         Replacement of Warrants. On receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction or mutilation of any Warrant and,
in the case of any such loss, theft or destruction of any Warrant, on delivery
of an indemnity agreement or security reasonably satisfactory in form and amount
to the Company or, in the case of any such mutilation, on surrender and
cancellation of such Warrant, the Company at its expense will execute and
deliver, in lieu thereof, a new Warrant of like tenor.

         Warrant Agent. The Company may, by written notice to each holder of a
Warrant, appoint an agent having an office in Boston, Massachusetts for the
purpose of issuing Common Stock (or Other Securities) on the exercise of the
Warrants pursuant to Section 1, exchanging Warrants pursuant to Section 10, and
replacing Warrants pursuant to Section 11, or any of the foregoing, and
thereafter any such issuance, exchange or replacement, as the case may be, shall
be made at such office by such agent.

         Remedies. The Company stipulates that the remedies at law of the holder
of this Warrant in the event of any default or threatened default by the Company
in the performance of or


<PAGE>   14
                                      -14-


compliance with any of the terms of this Warrant are not and will not be
adequate, and that such terms may be specifically enforced by a decree for the
specific performance of any agreement contained herein or by an injunction
against a violation of any of the terms hereof or otherwise.

         Negotiability, etc. This Warrant is issued upon the following terms, to
all of which each holder or owner hereof by the taking hereof consents and
agrees:

                  subject to the terms of the Stockholders' Agreement, title to
         this Warrant may be transferred by endorsement (by the holder hereof
         executing the form of assignment at the end hereof) and delivery in the
         same manner as in the case of a negotiable instrument transferable by
         endorsement and delivery; and

                  any person in possession of this Warrant properly endorsed for
         transfer to such person (including endorsed in blank) is authorized to
         represent himself as absolute owner hereof and is empowered to transfer
         absolute title hereto by endorsement and delivery hereof to a bona fide
         purchaser hereof for value; each prior taker or owner waives and
         renounces all of his equities or rights in this Warrant in favor of
         each such bona fide purchaser, and each such bona fide purchaser shall
         acquire absolute title hereto and to all rights represented hereby.

         Notices, etc. All notices and other communications from the Company to
the holder of this Warrant shall be mailed by first class registered or
certified mail, postage prepaid, at such address as may have been furnished to
the Company in writing by such holder or, until any such holder furnishes to the
Company an address, then to, and at the address of, the last holder of this
Warrant who has so furnished an address to the Company.

         Miscellaneous. This Warrant and any term hereof may be changed, waived,
discharged or terminated only by an instrument in writing signed by the party
against which enforcement of such change, waiver, discharge or termination is
sought. This Warrant shall be construed and enforced in accordance with and
governed by the laws of The Commonwealth of Massachusetts. The headings in this
Warrant are for purposes of reference only, and shall not limit or otherwise
affect any of the terms hereof. This Warrant is being executed as an instrument
under seal. The invalidity or unenforceability of any provision hereof shall in
no way affect the validity or enforceability of any other provision.

         Expiration. The right to exercise this Warrant shall expire at 5:00
p.m., Boston time, on the later of (i) March 31, 2005 or (ii) at such time as
all principal, premium (if any) and interest on the Notes (as defined in the
Agreement) is paid in full. Notwithstanding the foregoing, this Warrant shall
automatically be deemed to be exercised in full pursuant to the provisions of
Section 1.6 hereof, without any further action on behalf of the holder,
immediately prior to the time this Warrant would otherwise expire pursuant to
the preceding sentence.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]



<PAGE>   15
                                      -15-


         IN WITNESS WHEREOF, the Company has executed this Warrant under seal as
of the date first written above.

                                       ODYSSEY HEALTHCARE, INC.




                                       By:
                                          --------------------------------------
                                          Name:
                                          Title:



<PAGE>   16

                              FORM OF SUBSCRIPTION
                   (To be signed only on exercise of Warrant)

ODYSSEY HEALTHCARE, INC.

         The undersigned, the holder of the within Warrant, hereby irrevocably
elects to exercise this Warrant for, and to purchase thereunder, _________
shares of Common Stock of Odyssey HealthCare, Inc. and herewith makes payment of
$__________ therefor, and requests that the certificates for such shares be
issued in the name of, and delivered to ___________________, federal taxpayer
identification number _______________, whose address is _______________________.

Dated:

                                       -----------------------------------------
                                       (Signature must conform to name of holder
                                       as specified on the face of the Warrant)


                                       -----------------------------------------
                                                      (Address)

Signed in the presence of:

--------------------------------

                                   ----------

                               FORM OF ASSIGNMENT
                   (To be signed only on transfer of Warrant)

         For value received, the undersigned hereby sells, assigns, and
transfers unto __________, federal taxpayer identification number
________________, whose address is ______________, the right represented by the
within Warrant to purchase ______________ shares of Common Stock of Odyssey
HealthCare, Inc. to which the within Warrant relates, and appoints
________________ Attorney to transfer such right on the books of Odyssey
HealthCare, Inc. with full power of substitution in the premises.

Dated:
                                       -----------------------------------------
                                       (Signature must conform to name of holder
                                       as specified on the face of the Warrant)


                                       -----------------------------------------
                                                       (Address)

Signed in the presence of:

--------------------------------



<PAGE>   17

                           FORM OF NET ISSUE ELECTION
            (To be signed only on net issue exercise of the Warrant)


         The undersigned, the holder of the within Warrant, hereby irrevocably
elects to exercise this Warrant with respect to ______________ shares of Common
Stock of Odyssey HealthCare, Inc., pursuant to the net issuance provisions set
forth in Section 1.6 of this Warrant, and requests that the certificates for the
number of shares of Common Stock issuable pursuant to said Section 1.6 after
application of the net issuance formula to such _____________ shares to be
issued in the name of, and delivered to ________________________, federal
taxpayer identification number ________________, whose address is
_________________________________.


Dated:
                                       -----------------------------------------
                                       (Signature must conform to name of holder
                                       as specified on the face of the Warrant)


                                       -----------------------------------------
                                                       (Address)



<PAGE>   18

                             LIST OF WARRANT HOLDERS


<TABLE>
<CAPTION>
      CERTIFICATE                                                                                 NUMBER OF
        NUMBER                             HOLDER NAME                    DATE                      SHARES
      -----------                          -----------                    ----                    ---------
<S>                      <C>                                             <C>                      <C>
    W-1                  Capital Resource Lenders III, L.P.              7/1/98                   1,777,752

    W-2                  CRP Investment Partners III, L.L.C.             7/1/98                       4,456

    W-3                  Capital Resource Lenders III, L.P.             12/31/98                    160,909

    W-4                  CRP Investment Partners III, L.L.C.            12/31/98                        403

Total Outstanding                                                                                 1,943,520
</TABLE>