\[ -\left (a x^2+1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0291308 (sec), leaf count = 49
\[\left \{\left \{y(x)\to \frac {e^{-\frac {\sqrt {a} x}{2}} \left (c_2 e^{\sqrt {a} x}+\sqrt {a} c_1\right )}{\sqrt {a} \sqrt {x}}\right \}\right \}\]
✓ Maple : cpu = 0.056 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C2}\,\cosh \left ( {\frac {x}{2}\sqrt {a}} \right ) +{\it \_C1}\,\sinh \left ( {\frac {x}{2}\sqrt {a}} \right ) \right ) {\frac {1}{\sqrt {x}}}} \right \} \]