74.5.32 problem 32

Internal problem ID [15996]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 08:26:01 AM
CAS classification : [_linear]

\begin{align*} \left ({\mathrm e}^{t}+1\right ) y^{\prime }+{\mathrm e}^{t} y&=t \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

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

\[ y = \frac {t^{2}-4}{2+2 \,{\mathrm e}^{t}} \]

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 21

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

\[ y(t)\to \frac {t^2-4}{2 \left (e^t+1\right )} \]