74.3.3 problem 1 (c)

Internal problem ID [15863]
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 : 1 (c)
Date solved : Tuesday, January 28, 2025 at 08:10:34 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(t),t)=y(t)+1/(1-t),y(t), singsol=all)
 

\[ y = \left ({\mathrm e}^{-1} \operatorname {Ei}_{1}\left (t -1\right )+c_{1} \right ) {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 33

DSolve[D[y[t],t]==y[t]+1/(1-t),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (\int _1^t-\frac {e^{-K[1]}}{K[1]-1}dK[1]+c_1\right ) \]