74.3.24 problem 19

Internal problem ID [15884]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 08:17:14 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{t -3}&=\frac {1}{t -1} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 26

dsolve([diff(y(t),t)+1/(t-3)*y(t)=1/(t-1),y(-1) = 0],y(t), singsol=all)
 

\[ y = \frac {t -2 \ln \left (t -1\right )+1+2 \ln \left (2\right )+2 i \pi }{t -3} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 32

DSolve[{D[y[t],t]+1/(t-3)*y[t]==1/(t-1),{y[-1]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {\int _{-1}^t\frac {3-K[1]}{K[1]-1}dK[1]}{t-3} \]