\[ \left (-a x^2-2\right ) y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0166555 (sec), leaf count = 129
\[\left \{\left \{y(x)\to \frac {\sqrt {\frac {2}{\pi }} c_2 \sqrt {x} \left (i \sinh \left (\sqrt {a} x\right )-\frac {i \cosh \left (\sqrt {a} x\right )}{\sqrt {a} x}\right )}{\sqrt {-i \sqrt {a} x}}+\frac {\sqrt {\frac {2}{\pi }} c_1 \sqrt {x} \left (\frac {\sinh \left (\sqrt {a} x\right )}{\sqrt {a} x}-\cosh \left (\sqrt {a} x\right )\right )}{\sqrt {-i \sqrt {a} x}}\right \}\right \}\] ✓ Maple : cpu = 0.114 (sec), leaf count = 43
\[\left \{y \left (x \right ) = \frac {-c_{1} \left (a x -\sqrt {a}\right ) {\mathrm e}^{\sqrt {a}\, x}+c_{2} \left (a x +\sqrt {a}\right ) {\mathrm e}^{-\sqrt {a}\, x}}{x}\right \}\]