Internal problem ID [6978]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 247.
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}-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)-x^2*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x +2\right )}{x}+\frac {c_{2} {\mathrm e}^{x} \left (x -2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 57
DSolve[x^2*y''[x]-x^2*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(c_1-i c_2) \left (-e^x\right ) (x-2)-(c_1+i c_2) (x+2)}{\sqrt {\pi } \sqrt {-i x} \sqrt {x}} \\ \end{align*}