\[ x^2 y''(x)-\left (a x^2+2\right ) y(x)=0 \] ✓ Mathematica : cpu = 0.0203179 (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 = 0.088 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x}{{\rm e}^{\sqrt {a}x}} \left ( -ax+\sqrt {a} \right ) }+{\frac {{\it \_C2}}{x}{{\rm e}^{-\sqrt {a}x}} \left ( ax+\sqrt {a} \right ) } \right \} \]