74.5.31 problem 31

Internal problem ID [15995]
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 : 31
Date solved : Tuesday, January 28, 2025 at 08:26:00 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } t +y&=2 t \,{\mathrm e}^{t} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 18

dsolve([t*diff(y(t),t)+y(t)=2*t*exp(t),y(1) = -1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 19

DSolve[{t*D[y[t],t]+y[t]==2*t*Exp[t],{y[1]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

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