Internal problem ID [6160]
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`]]
\[ \boxed {y^{\prime }+y=2 x \,{\mathrm e}^{-x}+x^{2}} \]
✓ 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)
\[ y \left (x \right ) = x^{2}-2 x +{\mathrm e}^{-x} x^{2}+2+{\mathrm e}^{-x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 29
DSolve[y'[x]+y[x]==2*x*Exp[-x]+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (x^2+e^x \left (x^2-2 x+2\right )+c_1\right ) \]