OpenLLM-France/wikimedia huggingface dataset:
# Very Small Information Systems/SS2006/Creating a microphone for JOP

This is a decription on how to make a microphone module for the JOP Board
The objective with this article is to descibe how to make a simple analog to digital converter using the Sigma Delta converter model: Sigma-Delta ADC Tutorial
Following components are needed to make the hardware part of the analog to digital converter:
* A microphone
* Two resistors- one 100K and one 1M
* Two capacitors one 220 nF and one 47 pF
* One Printed Wiring Board(PWB) to assemble it all on

## The circuit diagram

Solder it all together and attach it to your JOP board, then you should end up with a result that looks like this.

## Audio in and out with Baseio

Connection of external components for a simple sigma-delta ADC and PWM DAC to the baseio board.
# Very Small Information Systems/Spring 2006/Group A/Intelligent Humidity and Heating Control

The background for the system is, that one of the authors of this article have experienced the problem with damage to a summerhouse, first hand. Due to the lack of any monitoring device, some of the wooden construction in the house incurred damage. This damage could possibly have been avoided had a monitoring device alerted the owners to the fact that border values was being exceeded.
Wooden houses are known to have problems with low temperatures and extremes of relative humidity. It is known that wooden houses, and in particular summerhouses, that are not occupied all year round, need to be monitored to make sure that humidity and temperature does not exceed certain levels. Therefore our systems primary goal is to help avoid woodwork damages caused by humidity. This is solved through monitoring and adjustment of the indoors climate. This is done through the use of intelligent humidity and temperature control, and remote monitoring by use of a built in webserver. In addition, the system is capable of logging data about its surrounding conditions, enabling improvement of the enclosed algorithms. To support the control of humidity, we have developed a range of hardware devices providing the necessary inputs and enabling the actual environment control.

## Papers

See our detailed projectplan using this link. The projectplan is now outdated, as the project has been handed in at the 31st of May 2006.
The handed in WoodSaver article is available here.
During the project, we have made three guides, one is for inserting figures in latex, by converting the figures to PDF. The other two are howto documents explaining how to construct a relay and an input simulator with a potentiometer and a voltage follower.
Sourcecode: check out our module 'WoodSaver' from the sourceforge.net project 'wsis' or use the web access.

### Hardware guides

The two hardware guides are available here:
* Howto: Construction of a 220V relay
* Howto: Construction of a voltage follower/input simulator

### Inserting Figures in Latex

An easy way of inserting a figure in latex is this:
* Print the figure to a .pdf file.
* Crop the PDF file by using Adobe Acrobat, so it only takes up the necessary space (Tools/Advanced editing/Crop tool).
* Save the PDF file in a subfolder of your latex directory called figures.
* To insert the figure in latex, insert the following:
* You can reference the figure by using the syntax
# Very Small Information Systems/Spring 2006/Group C Barcode
## Group C - Barcode recognition under resource limitations

NOTE NOTE final exam/evaluation on June 21st. This page will be updated thereafter, and thereby include the lessons learned from the feedback. NOTE NOTE
Morten Okholm, Troels Nielsen and Søren Krabbe.
Currently the project is addressing two problems:
a) Is it realistic to do content-filtering on a stream of images in real time under heavy resource limitations?
b) How resource intensive is recognition of formal and known patterns in single images?
For more info, check out our module 'GroupC' from the sourceforge.net project 'wsis':
The unfinished article: Documents\Working\Article\VSIS_article_groupC.[pdf|tex]
Java code is in: Java\Barcode_Recognition
Currently we're experimenting quite a lot with our Java code, so it's not runnable on JOP and it might seem a bit messy - sorry.
If you just want it running, run.bat in the Java folder could very well be your friend:
run pc will process all images found in the folder 'Testimages' and print the results
run jop will try (and succeed!) to recognize a simple hardcoded imageline. Not much fun at the moment!
Enjoy!
# Very Small Information Systems/SS2006/Group D Jop Voice Recognition
## Group D - Voice recognition

Christian B. Olsen, Jacob H. Svalastoga, Michael J. Moltke and Thomas S. Olesen

### Paper Abstract

It has always been an issue in different situations to be able to identify an individual. Today when more and more interactions take place electronically it becomes increasingly relevant to be able to identify an individual in this way. The ultimate way to do this is by using biometrics. In this paper we will concentrate on the specific field in biometrics called speaker recognition, identifying a person from the sound of their voice. We will extract the easily found amplitude values per timeperiod from a normal voicesample soundwave. With the Fast Fourier Transform theorem we move from the time domain to the frequency domain, and by using the Nearest Neighbour data mining algorithm we are finally able to distinquish the voice of one individual from another.

#### Paper and Source Code

* Paper and source code is no longer online
** Vsis-project-group-d.pdf - The paper
** FFTLib CSharpCode.rar - Source code for sending sound to the JOP
** JopServerWithFourier.rar - Source code for the JOP server

### Previous project idea

Our main scope is to provide a dependable real-time distance calculation using laser equipment. In the end we hope to mount this equipment on a remote-controlled vehicle and make it able to brake at specified ranges from obstacles. The software will be developed in Java so it can run on a JOP. Project was abandoned due to the cost involved of acquiring a laser that could meet the requirements.
# Very Small Information Systems/RA

Here you find a list of projects as follow-up to the VSIS class. Some of these projects are funded.

### Clinit Order (Tools1)

Analyze the application and produce a correct order of class initialization methods. Report an error when this order cannot be determined.

### Classfile optimization (Tools1)

For embedded systems the memory footprint is of primary importance. However, the standard library contains many methods or fields that are probably never used by the application. JOPizer already analyzes the application and removes unused classes. The project here is to extend this optimization to remove unused methods and fields.

### Java TCP/IP (CLDC2)

A TCP/IP stack written completely in Java based on ejip. API for the TCP/IP stack as in javax.microedition.io, part of CLDC. The TCP/IP stack has to be implemented for real-time applications (time predictable code and memory usage).

### Java bytecode optimizer

The standard Java compiler (javac) performs no optimization at all. Optimization is postboned to the JIT compiler. For a Java processor (or an interpreting JVM) this is not an optimal solution. The idea is to implement standard compiler optimizations and processor specific optimizations at the bytecode level. See: JVM Specification, Byte Code Engineering Library and ASM

### JOP Debugger (Tools2)

A debugger inteface, the JavaTM Debug Wire Protocol or a different solution with Eclipse , for JOP.

### Real-time Library (CLDC1)

Implementation of the standard library (JDK CLDC subset) for real-time systems on JOP based on GNU Classpath (Java).

### JVM Test Framework (CLDC3)

There is no free test suite available to verify the correctness of the JVM. Implementation of test cases to verify that an implementation of a JVM (Java Virtal Machine) confirms to the JVM specification. Test of JOP and other JVMs.

### Library Test Cases (CLDC3)

Adaption of available JDK test cases for the embedded domain (JDK subset) and implementation of missing test cases. Test of JOP and other JVM implementations.

### Documentation of Sample Applications (DOC1)

HOW TO documents with sample applications for an easy start with JOP. Shall be a beginning of a user manual.

### WCET Analysis of Java Applications

Worst-case execution time (WCET) estimates are essential for real-time systems. The theory for static WCET analysis is mature. However, the tools are still missing. The tool shall provide WCET estimates for Java real-time applications running on a Java processor (JOP) that is designed to be an easy target (thesis) for WCET analysis.

### SoftFloat

Porting a software implementation of floating-point operations (SoftFloat) from C to Java. Extensive tests of the implementation. Part of the implementation is done, you are not starting from scratch.
# Six Sigma
## Six Sigma

Six Sigma was created by Bill Smith at Motorola in 1986 it was developed as a way for measuring defects and improving quality. The aim of Six Sigma is to deliver high performance. The methods aim to reduce defects in production to acceptable levels (3.4 per million).
Defined as a measure of quality that strives for near perfection, six sigma is a disciplined, data-driven approach and methodology for eliminating defects (driving towards six standard deviations between the mean and the nearest specification limit) in any process -- from manufacturing to transactional and from product to service. To achieve six sigma, a process must not produce more than 3.4 defects per million opportunities.
In last decade, we have witness the close convergence of Lean (originated at Toyota, japan) with Six Sigma. It is very well-known that a far-reaching performance is achieved by the use of Six Sigma and Lean to reduce waste. This in turn reduces cost, an important factor in determining the survival of an enterprise. Manufacturing with Lean in mind, has certain features such as reduced lead times of processes, faster delivery, improved quality of end products, reduction in inventory such as the work-in-process (WIP), low customer service activities, core materials, and products at all customer interfaces. This gives room for incorporating changes.
Most of the top companies listed by Fortune 500 magazine integrate Lean and Six Sigma ideologies in all of their operations. Some of them are 3M, Amazon.com, Bank of America, Boeing Frontiers, Caterpillar Inc., Dell, Eastman Kodak Company, General Electric, Honeywell, and so on. In fact, IBM, Motorola, and GE, etc. offer solutions to businesses based on their type of industries. All these Fortune 500 companies have been extremely quick in bringing Lean Six Sigma best practices to their India operations too. They have been followed by the implementation of the quality process by several big names in the IT sphere like Wipro, TCS and Infosys.
The DMAIC method:
The LSS methodology uses a comprehensive methodology incorporating the key elements of both, Six Sigma and Lean, as each stage can gain from the respective techniques. Today, the Six Sigma road map of define, measure, analyze, improve, and control (DMAIC) includes Lean concepts of empowerment and education of everyone in the organization to identify and eliminate non-value adding activities. The integration of the two methodologies attempts to provide empowerment even at the higher level process analysis stages, so that employees have true ownership of the process.

## See Also

* Wikipedia: Six Sigma
# Skewness

Skewness refers to asymmetry (or "tapering") in the distribution of sample data:
* negative skew: The left tail is longer; the mass of the distribution is concentrated on the right of the figure. It has a few relatively high values. The distribution is said to be left-skewed. In such a distribution, usually (but not always) the mean is lower than the median, and the median is lower than the mode; in which case the skewness is lower than zero.
* positive skew: The right tail is longer; the mass of the distribution is concentrated on the left of the figure. It has a few relatively low values. The distribution is said to be right-skewed. In such a distribution, usually (but not always) the mean is greater than the median, or equivalently, the mean is greater than the mode; in which case the skewness is greater than zero.
The relationship between mean and median is not sufficient to make a statement about the skewness of the distribution, but it can serve as an indicator.
In a skewed (unbalanced, lopsided) distribution, the mean is farther out in the long tail than is the median. If there is no skewness or the distribution is symmetric like the bell-shaped normal curve then the mean = median = mode. Usually there are three ways in which a set of data can be analyzed for its distribution: 1.By the range: This gives a rough idea of the spread of data but it is affected by extreme values. It is generally only used with small data groups together with either median or mode. 2.The interquartile range(IQR): It is not affected by extreme values and tells you how spread out the middle 50% of the observations are. The IQR is often used together with the median when data are skewed. 3.The mean with standard deviation: It is generally used when the data are symmetrical and the data size is not small.
# Skeletal System/PRICE

* P = Protect
* R = Rest
* I = Ice
* C - Compress
* E = Elevate
# Size Exclusion Chromatography
## Introduction

This technique, also known by the name Gel Permeation Chromatography (GPC) is used to determine the molar mass distribution of polymers in solution.
A polymer sample in solution is injected on top of a column. A flow of liquid (eluent) takes the sample through the column where the molecules are separated according to their size in solution. The largest molecules elute first.
The separation principle is an exclusion of large molecules from pores in the matrix of the particles in the column, letting them pass the column in a shorter time.
The equipment is in principle a liquid chromatograph, often with the option that samples can be run at elevated temperatures. Polyethylene for example can be run at 140°C in trichlorobenzene. The separation is normally isocratic, using only one eluent.
The detector is often a refractive index detector or a light scattering detector, but any LC detector could be used. The advantage of a light scattering detector measuring in a minimum of two angles is that the absolute molar mass can be determined directly.
Since the diameter of a polymer molecule in solution is dependent on the solvent, all other detectors have to be calibrated using polymer standards of differing molar mass with narrow distributions.
# Skeletal System/True or False

True 1. Your skeletal system is made up of bones, joints, and connective tissue. True 2. The vertebrae supports your body and protects your spinal cord. False 3. Tendons connect bone to bone. False 4. Osteoporosis is when a bone is pushed out of its joint. True 5. Your nose and ears are made of cartilage. True 6. Arthritis is when a person has swollen or stiff joints. True 7. A baby’s skeleton consists of over 300 bones. True 8. Joints are the points at which bones meet. False 9. Ligaments connect muscle to bone. False 10. The bones of your cranium protect your heart and lungs. True 11. Making blood cells is a function or job of the skeletal system. True 12. Blood cells are made in the bone marrow. True 13. Exercise, good posture, and having a healthy diet are ways of keeping the skeletal system healthy. True 14. The skeleton supports our body and gives it shape. False 15. The mandible and clavicle make up the upper and lower jawbones.
BONUS:
What are the 4 functions of the skeletal system? Supports the body by providing a framework, Protects the internal organs, Store minerals, and Makes blood cells in the blood marrow.
# University of Florida/Egm4313/s12.team11.gooding/R3
## Problem 3.7

Solved By Kyle Gooding

### Problem Statement

Expand the series on both sides of (1),(2) pg. 7-12b to verify these equalities. (1)

#### Given

$\sum _{j=2}^{5}C_{j}*j(j-1)x^{j-2}=\sum _{j=0}^{3}C_{j+2}*(j+2)(j+1)x^{j}$
(2) $\sum _{j=1}^{5}C_{j}*jx^{j-1}=\sum _{j=0}^{4}C_{j+1}*(j+1)x^{j}$

#### Solutions

Expanding both sides of (1) results in: $\sum _{j=2}^{5}C_{j}*j(j-1)x^{j-2}=C_{2}(2)(2-1)x^{0}+C_{3}(3)(3-1)x^{1}+C_{4}(4)(4-1)x^{2}+C_{5}(5)(5-1)x^{3}$ $\sum _{j=0}^{3}C_{j}(j+2)(j+1)x^{j}=C_{0+2}(0+2)(0+1)x^{0}+C_{1+2}(1+2)(1+1)x^{1}+C_{2+2}(2+2)(2+1)x^{2}+C_{3+2}(3+2)(3+1)x^{3}$
Simplifying: $\sum _{j=2}^{5}C_{j}*j(j-1)x^{j-2}=C_{2}(2)+C_{3}6x+C_{4}12x^{2}+C_{5}20x^{3}$ $\sum _{j=0}^{3}C_{j}(j+2)(j+1)x^{j}=C_{2}(2)+C_{3}6x+C_{4}12x^{2}+C_{5}20x^{3}$
Expanding both sides of (2) results in: $\sum _{j=1}^{5}C_{j}*jx^{j-1}=C_{1}(1)x^{0}+C_{2}(2)x^{1}+C_{3}(3)x^{2}+C_{4}(4)x^{3}+C_{5}(5)x^{4}$ $\sum _{j=0}^{4}C_{j+1}*(j+1)x^{j}=C_{0+1}(0+1)x^{0}+C_{1+1}(1+1)x^{1}+C_{1+2}(2+1)x^{2}+C_{2+2}(3+1)x^{3}+C_{3+2}(4+1)x^{4}$
Simplifying: $\sum _{j=1}^{5}C_{j}*jx^{j-1}=C_{1}(1)+C_{2}(2)x^{1}+C_{3}(3)x^{2}+C_{4}(4)x^{3}+C_{5}(5)x^{4}$ $\sum _{j=1}^{5}C_{j}*jx^{j-1}=C_{1}(1)+C_{2}(2)x^{1}+C_{3}(3)x^{2}+C_{4}(4)x^{3}+C_{5}(5)x^{4}$
Egm4313.s12.team11.gooding 23:49, 19 February 2012 (UTC)
# University of Florida/Egm4313/s12.team11.gooding.k/R7
##### Scalar Product

$<f,g>=\int _{a}^{b}f(x)g(x)\ dx\!$
$<f,g>=\int _{-2}^{10}x\cos(x)\ dx\!$
Using integration by parts;
$<f,g>=[x\sin(x)+\cos(x)]_{-2}^{10}$

##### Magnitude

$\|f\|=<f,f>^{1/2}=\int _{a}^{b}f^{2}(x)\ dx\!$
$=\int _{-2}^{10}[\cos(x)]^{2}\ dx\!$
$=[.5(x+\sin(x)\cos(x)|_{-2}^{10}]^{1/2}$
$\|g\|=\int _{a}^{b}g^{2}(x)\ dx\!$
$=\int _{-2}^{10}x^{2}\ dx$ $=[x^{3}/3]_{-2}^{10}$

##### Angle Between Functions

$cos(\theta )={\frac {<f,g>}{\|f\|\|g\|}}\!$
$cos(\theta )={\frac {-7.68}{{\frac {1008}{3}}(2.457)}}$
# University of Florida/Egm4313/s12.team11.gooding/R2/2.1

Problem R2.1

## Part 1
### Problem Statement

Given the two roots and the initial conditions:
$\lambda _{1}=-2,\lambda _{2}=5\!$ $y(0)=1,y'(0)=0\!$
Find the non-homogeneous L2-ODE-CC in standard form and the solution in terms of the initial conditions and the general excitation $r(x)\!$. Consider no excitation:
$r(x)=0\!$ Plot the solution

### Solution
#### Characteristic Equation:

$(\lambda -\lambda _{1})(\lambda -\lambda _{2})=0\!$
$(\lambda +2)(\lambda -5)=\lambda ^{2}+2\lambda -5\lambda -10=0\!$

#### Homogeneous Solution:

$y_{h}(x)=c_{1}e^{-2x}+c_{2}e^{5x}\!$ $y(x)=c_{1}e^{-2x}+c_{2}e^{5x}+y_{p}(x)\!$ Since there is no excitation,
$y_{p}(x)=0\!$

#### Substituting the given initial conditions:

$y(0)=1\!$
$y'(0)=0\!$
Solving these two equations for $c_{1}\!$ and $c_{2}\!$ yields:

#### Final Solution
## Part 2
### Problem Statement

Generate 3 non-standard (and non-homogeneous) L2-ODE-CC that admit the 2 values in (3a) p.3-7 as the 2 roots of the corresponding characteristic equation.

### Solutions

$2(\lambda +2)(\lambda -5)=2\lambda ^{2}+4\lambda -10\lambda -20=0\!$
$3(\lambda +2)(\lambda -5)=3\lambda ^{2}+6\lambda -15\lambda -30=0\!$
$4(\lambda +2)(\lambda -5)=4\lambda ^{2}+8\lambda -20\lambda -40=0\!$
--Egm4313.s12.team11.gooding 02:01, 7 February 2012 (UTC)
# University of Florida/Egm4313/s12.team11.gooding/R6
## R6.3
### Problem Statement

Page 491, #15,17. Plot the truncated Fourier series for n=2,4,8.

### Solution

15.
$f(x)=\left\{{\begin{matrix}-x-\pi ,-\pi <x<-\pi /2\\x,-\pi /2<x<\pi /2\\\pi -x,\pi /2<x<\pi \end{matrix}}\right.$
Since $f(-x)=-f(x)$, the function is odd.
$a_{0}=(1/\pi )*[-1\int _{-\pi }^{-\pi /2}(x+\pi )dx+\int _{-\pi /2}^{\pi /2}(x)dx+\int _{\pi /2}^{\pi }(\pi -x)dx]$ After simplification, $a_{0}=0$ . Using Equation (5) on page 490, the exapansion becomes; $f(x)=8k/\pi ^{2}[sin(\pi *x/L)-sin(3\pi *x/L)/9...)$ With $L=\pi ,k=\pi /2$ this becomes; $f(x)=4/\pi (sinx-sin(3x)/9+sin(5x)/25-sin(6x)/36....)$ for n is "odd". This means when n is even, $f(x)=0$
17. $f(x)=1-|x|,-1\leq x\leq 1$
$f(x)=\left\{{\begin{matrix}1+x-\pi ,-1<x<0\\1-x,0<x<1\\\end{matrix}}\right.$
$a_{0}=1/2[\int _{-1}^{0}(1+x)dx+\int _{0}^{1}(1-x)dx]$ $a_{0}=1/2[1-1/2+1-1/2]$
$a_{n}=1/1[\int _{-1}^{0}(1+x)cos(n\pi *x/1)dx+\int _{0}^{1}(1-x)cos(n\pi *x/1)dx]$ Simplifying results in; $a_{n}=2[1/(n^{2}\pi ^{2})_{-1)^{n}/(n^{2}\pi ^{2})]$ So,
when n is odd. $b_{n}=1/1[\int _{-1}^{0}(1+x)sin(n\pi *x/1)dx+\int _{0}^{1}(1-x)sin(n\pi *x/1)dx]$ Simplifying results in;
$f(x)=1/2+\sum _{n=0}^{\infty }4/(n^{2}\pi ^{2})*cos(n\pi *x)$
Since $a_{n}=0$ for even n, $f(x)$ becomes $f(x)=1/2$ for even n.
# University of Florida/Egm4313/s12.team11.imponenti/R1.3
## Report 1,problem 3
### Problem Statement

For the spring-dashpot-mass system shown, draw the FBDs and derive the following equation of motion
$my''+f_{I}=f(t)$

### Free Body Diagram

Where f$_I$ is the resistive force from both the spring and dash-pot and f(t) is our applied force.

### Kinetics

Newton's second law of motion in the y-direction
Σ$F_{y}=ma=f(t)-f_{I}$ where $a=y''$
which can be re-written as
Egm4313.s12.team11.imponenti 03:01, 30 January 2012 (UTC)
# University of Florida/Egm4313/s12.team11.gooding/R2/2.8

Problem R2.8

### Problem Statement

Find a general solution. Check your answer by substitution.

## Problem 8

$y''+y'+3.25y=0\!$
Let: $\lambda =d/dx\!$

#### Characteristic Equation

$\lambda ^{2}+\lambda +3.25=0\!$ Using the quadratic equation to find roots we get: $\lambda _{1}={\frac {-1+i{\sqrt {}12)}{2}}\!$ $\lambda _{2}={\frac {-1-i{\sqrt {}12)}{2}}\!$ Therefore:

#### Check By Substitution

$y'(x)=-{\frac {1}{2}}e^{-{\frac {1}{2}}x}(c_{1}\cos(x{\sqrt {3}})+c_{2}\sin(x{\sqrt {3}})+e^{-{\frac {1}{2}}x}(-{\sqrt {3}}c_{1}\sin {{\sqrt {3}}x}+{\sqrt {3}}c_{1}\cos {{\sqrt {3}}x})\!$ $y''(x)={\frac {1}{4}}e^{-{\frac {1}{2}}x}(c_{1}\cos(x{\sqrt {3}})+c_{2}\sin(x{\sqrt {3}})-{\frac {1}{2}}e^{-{\frac {1}{2}}x}(-{\sqrt {3}}c_{1}\sin {{\sqrt {3}}x}+{\sqrt {3}}c_{1}\cos {{\sqrt {3}}x})-\!$ ${\frac {1}{2}}e^{-{\frac {1}{2}}x}(-{\sqrt {3}}c_{1}\sin {{\sqrt {3}}x}+{\sqrt {3}}c_{1}\cos {{\sqrt {3}}x})e^{-{\frac {1}{2}}x}(-3c_{1}\cos(x{\sqrt {3}})-3c_{2}\sin(x{\sqrt {3}})\!$ Substituting $y,y',y''\!$ into the original equation, the result is

## Problem 15

$y''+0.54y'+(0.0729+\pi )y=0\!$ Let: ${\frac {d}{dx}}=\lambda \!$

### Characteristic Equation

$\lambda ^{2}+0.54\lambda +(0.0729+\pi )=0\!$ Using the quadratic equation to find roots we get: $\lambda _{1}={\frac {-0.27+i{\sqrt {}\pi )}{2}}\!$ $\lambda _{2}={\frac {-0.27-i{\sqrt {}\pi )}{2}}\!$ Therefore:

#### Check By Substitution

$y'(x)=-0.27e^{-0.27x}(c_{1}\cos(x{\sqrt {\pi }})+c_{2}\sin(x{\sqrt {\pi }})+e^{-0.27x}(-{\sqrt {\pi }}c_{1}\sin {{\sqrt {\pi }}x}+{\sqrt {\pi }}c_{1}\cos {{\sqrt {\pi }}x})\!$
$y''(x)=0.0729e^{-0.27x}(c_{1}\cos(x{\sqrt {\pi }})+c_{2}\sin(x{\sqrt {\pi }})-0.27e^{-0.27x}(-{\sqrt {\pi }}c_{1}\sin {{\sqrt {\pi }}x}+{\sqrt {\pi }}c_{1}\cos {{\sqrt {\pi }}x})-\!$
$0.27e^{-0.27x}({\sqrt {\pi }}c_{1}\sin {{\sqrt {\pi }}x}+{\sqrt {\pi }}c_{1}\cos {{\sqrt {\pi }}x})+e^{-0.27x}(-\pi (c_{1}\cos(x{\sqrt {\pi }}))-\pi (c_{2}\sin(x{\sqrt {\pi }})))\!$
Substituting $y,y',y''\!$ into the original equation, the result is
Egm4313.s12.team11.gooding 03:41, 7 February 2012 (UTC)