\[ \left (a^2 x^2-6\right ) y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.021205 (sec), leaf count = 79
\[\left \{\left \{y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \sqrt {x} \left (\left (c_1 \left (a^2 x^2-3\right )+3 a c_2 x\right ) \sin (a x)+\left (-a^2 c_2 x^2+3 a c_1 x+3 c_2\right ) \cos (a x)\right )}{(a x)^{5/2}}\right \}\right \}\]
✓ Maple : cpu = 0.263 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {\it \_C1}\,{a}^{2}{x}^{2}+3\,{\it \_C2}\,ax-3\,{\it \_C1} \right ) \cos \left ( ax \right ) +\sin \left ( ax \right ) \left ( {\it \_C2}\,{a}^{2}{x}^{2}-3\,{\it \_C1}\,ax-3\,{\it \_C2} \right ) }{{x}^{2}}} \right \} \]