Internal problem ID [3111]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 11, page 49
Problem number: 2(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: 22
dsolve(diff(y(x),x)+y(x)=2*x*exp(-x)+x^2,y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{2}+c_{1} \right ) {\mathrm e}^{-x}+x^{2}-2 x +2 \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 29
DSolve[y'[x]+y[x]==2*x*Exp[-x]+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (x^2+e^x \left (x^2-2 x+2\right )+c_1\right ) \]