Internal problem ID [7195]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 474.
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 }-2 x y^{\prime }-\left (x^{2}-2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-(x^2-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \sinh \relax (x )+c_{2} x \cosh \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 25
DSolve[x^2*y''[x]-2*x*y'[x]-(x^2-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x} x+\frac {1}{2} c_2 e^x x \\ \end{align*}