Internal problem ID [6171]
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`]]
\[ \boxed {4 y+y^{\prime }={\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(y(x),x)+4*y(x)=exp(-x),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{3 x}-1\right ) {\mathrm e}^{-4 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 21
DSolve[{y'[x]+4*y[x]==Exp[-x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-4 x} \left (e^{3 x}-1\right ) \]