Internal problem ID [5407]
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: 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-2 \,{\mathrm e}^{-x} x -x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x)+y(x)=2*x*exp(-x)+x^2,y(x), singsol=all)
\[ y \relax (x ) = x^{2}-2 x +x^{2} {\mathrm e}^{-x}+2+{\mathrm e}^{-x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 24
DSolve[y'[x]+y[x]==2*x*Exp[-x]+x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (x^2+c_1\right )+(x-2) x+2 \\ \end{align*}