\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( a{x}^{2}+2 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.018002 (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 = 0.062 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x}{{\rm e}^{\sqrt {a} x}} \left ( -ax+\sqrt {a} \right ) }+{\frac {{\it \_C2}}{x}{{\rm e}^{- \sqrt {a}x}} \left ( ax+\sqrt {a} \right ) } \right \} \]