Internal problem ID [14234]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y=4 t \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(t),t)-y(t)=4*t*exp(-t),y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{1} {\mathrm e}^{2 t}-2 t -1\right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 24
DSolve[y'[t]-y[t]==4*t*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \left (-2 t+c_1 e^{2 t}-1\right ) \]