3.15 problem 2(e)

Internal problem ID [5418]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number: 2(e).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {y^{\prime }+4 y-{\mathrm e}^{-x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 16

dsolve([diff(y(x),x)+4*y(x)=exp(-x),y(0) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {\left ({\mathrm e}^{3 x}-1\right ) {\mathrm e}^{-4 x}}{3} \]

Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 21

DSolve[{y'[x]+4*y[x]==Exp[-x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} e^{-4 x} \left (e^{3 x}-1\right ) \\ \end{align*}