Internal problem ID [13829]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {y}{-3+t}=\frac {1}{t -1}} \] With initial conditions \begin {align*} [y \left (-1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
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: 0.034 (sec). Leaf size: 27
DSolve[{y'[t]+1/(t-3)*y[t]==1/(t-1),{y[-1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t-2 \log (t-1)+2 i \pi +1+\log (4)}{t-3} \]