\[ x^2 y''(x)-\left (a x^2+2\right ) y(x)=0 \] ✓ Mathematica : cpu = 0.0192093 (sec), leaf count = 88
\[\left \{\left \{y(x)\to -\frac {i \sqrt {\frac {2}{\pi }} \sqrt {x} \left (\left (c_1+i \sqrt {a} c_2 x\right ) \sinh \left (\sqrt {a} x\right )-\left (\sqrt {a} c_1 x+i c_2\right ) \cosh \left (\sqrt {a} x\right )\right )}{\left (-i \sqrt {a} x\right )^{3/2}}\right \}\right \}\]
✓ Maple : cpu = 0.131 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\it \_C2}\, \left ( ax+\sqrt {a} \right ) {{\rm e}^{-\sqrt {a}x}}-{\it \_C1}\,{{\rm e}^{\sqrt {a}x}} \left ( ax-\sqrt {a} \right ) \right ) } \right \} \]