Internal problem ID [6994]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 263.
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 }+y^{\prime } x^{2}+\left (-2+x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)+x^2*diff(y(x),x)+(x-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+\frac {c_{2} {\mathrm e}^{-x} \left (x^{2}+2 x +2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 28
DSolve[x^2*y''[x]+x^2*y'[x]+(x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1-c_2 e^{-x} (x (x+2)+2)}{x} \\ \end{align*}