Internal problem ID [4141]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22, problem 19, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }-y-x^{2} {\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=x^2*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+c_{2} x +\frac {{\mathrm e}^{-x} \left (x +1\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 27
DSolve[x^2*y''[x]+x*y'[x]-y[x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^2+e^{-x} (x+1)+c_1}{x} \\ \end{align*}