\[ -\left (a x^2+1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0269738 (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 = 0.096 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={{\it \_C1}\sinh \left ( {\frac {x}{2}\sqrt {a}} \right ) {\frac {1}{\sqrt {x}}}}+{{\it \_C2}\cosh \left ( {\frac {x}{2}\sqrt {a}} \right ) {\frac {1}{\sqrt {x}}}} \right \} \]