\[ \left (a^2 x^2-6\right ) y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.014096 (sec), leaf count = 114
\[\left \{\left \{y(x)\to \frac {\sqrt {\frac {2}{\pi }} c_1 \sqrt {x} \left (\frac {3 \sin (a x)}{a^2 x^2}-\sin (a x)-\frac {3 \cos (a x)}{a x}\right )}{\sqrt {a x}}+\frac {\sqrt {\frac {2}{\pi }} c_2 \sqrt {x} \left (-\frac {3 \cos (a x)}{a^2 x^2}-\frac {3 \sin (a x)}{a x}+\cos (a x)\right )}{\sqrt {a x}}\right \}\right \}\] ✓ Maple : cpu = 0.369 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {\it \_C1}\,{a}^{2}{x}^{2}+3\,{\it \_C2}\,ax-3\,{\it \_C1} \right ) \cos \left ( ax \right ) +\sin \left ( ax \right ) \left ( {\it \_C2}\,{a}^{2}{x}^{2}-3\,{\it \_C1}\,ax-3\,{\it \_C2} \right ) }{{x}^{2}}} \right \} \]