74.5.5 problem 5

Internal problem ID [15969]
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 : 5
Date solved : Tuesday, January 28, 2025 at 08:25:05 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=4 t \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(t),t)-y(t)=4*t*exp(-t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 29

DSolve[D[y[t],t]-y[t]==4*t*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (\int _1^t4 e^{-2 K[1]} K[1]dK[1]+c_1\right ) \]