5.5 problem 5

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]
 

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