74.11.54 problem 62 (e)

Internal problem ID [16304]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 62 (e)
Date solved : Tuesday, January 28, 2025 at 09:02:13 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 22

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

\[ y(t)\to \frac {1}{2} e^{-4 t} \left (t^2+2 c_1\right ) \]