\[ \left (a^2 x^2-6\right ) y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0136581 (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 = 0.21 (sec), leaf count = 53
\[y \relax (x ) = \frac {\left (a^{2} x^{2} c_{1}+3 a x c_{2}-3 c_{1}\right ) \cos \left (a x \right )+\sin \left (a x \right ) \left (a^{2} x^{2} c_{2}-3 a x c_{1}-3 c_{2}\right )}{x^{2}}\]