50.3.15 problem 2(e)

Internal problem ID [7839]
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)
Date solved : Monday, January 27, 2025 at 03:24:29 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 21

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

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