\[ a y(x)+\left (x^2+1\right ) y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.0141235 (sec), leaf count = 30
\[\left \{\left \{y(x)\to c_1 \cos \left (\sqrt {a} \sinh ^{-1}(x)\right )+c_2 \sin \left (\sqrt {a} \sinh ^{-1}(x)\right )\right \}\right \}\] ✓ Maple : cpu = 0.085 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( \sqrt {a}{\it Arcsinh} \left ( x \right ) \right ) +{\it \_C2}\,\cos \left ( \sqrt {a}{\it Arcsinh} \left ( x \right ) \right ) \right \} \]