Internal problem ID [14572]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+4 y=t \,{\mathrm e}^{-4 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(t),t)+4*y(t)=t*exp(-4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (t^{2}+2 c_{1} \right ) {\mathrm e}^{-4 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 22
DSolve[y'[t]+4*y[t]==t*Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-4 t} \left (t^2+2 c_1\right ) \]