Internal problem ID [8161]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 686.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x^{2}-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1} \left (x +2\right )}{x}+\frac {c_{2} {\mathrm e}^{x} \left (x -2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 72
DSolve[x^2*y''[x]-x^2*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2 e^{x/2} \left ((c_1 x+2 i c_2) \cosh \left (\frac {x}{2}\right )-(i c_2 x+2 c_1) \sinh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x} \sqrt {x}} \]