Internal problem ID [7399]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 680.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)+x^2*diff(y(x),x)-(2+x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-x}}{x}+\frac {c_{2} \left (x^{2}-2 x +2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 30
DSolve[x^2*y''[x]+x^2*y'[x]-(2+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} \left (c_2 e^x ((x-2) x+2)+c_1\right )}{x} \\ \end{align*}