Internal problem ID [7064]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 335.
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 }+\left (x^{2}-2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x$2)+(x^2-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x \cos \relax (x )-\sin \relax (x )\right )}{x}+\frac {c_{2} \left (\cos \relax (x )+\sin \relax (x ) x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 42
DSolve[x^2*y''[x]+(x^2-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {2}{\pi }} ((c_1 x+c_2) \cos (x)+(c_2 x-c_1) \sin (x))}{x} \\ \end{align*}