Therefore I think that there must be a different reason for the 'problem of equal k10 and k01'. Equal values of k10 and k01 are relatively frequently encountered. Therefore I do not understand the relative extensive literature on the pharmacokinetic analysis for the special case that k10 and k01 are equal. In my opinion, this situation is mainly an artifact of the fitting procedures. Therefore I would suggest not to focus on equations for this special case, but on procedures to avoid, or reduce, the occurence of equal k10 and k01.
Any suggestion is welcomed.
Anomalous parameter estimates in the one-compartment model with first order absorption. J Pharm Pharmacol 45 934-936. J Pharmacokin Biopharm 24 79-101. This software is based on modeling transfer functions in the complex domain. The functions of that type are called the disposition functions in pharmacokinetic literature.