\[ \left (a x^2+1\right ) y''(x)+a x y'(x)+b y(x)=0 \] ✓ Mathematica : cpu = 0.0384806 (sec), leaf count = 52
\[\left \{\left \{y(x)\to c_2 \sin \left (\frac {\sqrt {b} \sinh ^{-1}\left (\sqrt {a} x\right )}{\sqrt {a}}\right )+c_1 \cos \left (\frac {\sqrt {b} \sinh ^{-1}\left (\sqrt {a} x\right )}{\sqrt {a}}\right )\right \}\right \}\]
✓ Maple : cpu = 0.024 (sec), leaf count = 63
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C1}\, \left ( \left ( \sqrt {a}x+\sqrt {a{x}^{2}+1} \right ) ^{{i\sqrt {b}{\frac {1}{\sqrt {a}}}}} \right ) ^{2}+{\it \_C2} \right ) \left ( \left ( \sqrt {a}x+\sqrt {a{x}^{2}+1} \right ) ^{{i\sqrt {b}{\frac {1}{\sqrt {a}}}}} \right ) ^{-1}} \right \} \]