\[ \boxed { 4\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( a{x}^{2}+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.028504 (sec), leaf count = 51 \[ \left \{\left \{y(x)\to \frac {c_1 e^{-\frac {\sqrt {a} x}{2}}}{\sqrt {x}}+\frac {c_2 e^{\frac {\sqrt {a} x}{2}}}{\sqrt {a} \sqrt {x}}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={{\it \_C1}\sinh \left ( {\frac {x}{2} \sqrt {a}} \right ) {\frac {1}{\sqrt {x}}}}+{{\it \_C2}\cosh \left ( { \frac {x}{2}\sqrt {a}} \right ) {\frac {1}{\sqrt {x}}}} \right \} \]