\[ \left (a^2 x^2-6\right ) y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0149217 (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 = 0.246 (sec), leaf count = 53
\[\left \{y \left (x \right ) = \frac {\left (c_{1} a^{2} x^{2}+3 c_{2} a x -3 c_{1}\right ) \cos \left (a x \right )+\left (c_{2} a^{2} x^{2}-3 c_{1} a x -3 c_{2}\right ) \sin \left (a x \right )}{x^{2}}\right \}\]