\[ \left (a x^2+1\right ) y''(x)+a x y'(x)+b y(x)=0 \] ✓ Mathematica : cpu = 0.0236036 (sec), leaf count = 52
\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {\sqrt {b} \sinh ^{-1}\left (\sqrt {a} x\right )}{\sqrt {a}}\right )+c_2 \sin \left (\frac {\sqrt {b} \sinh ^{-1}\left (\sqrt {a} x\right )}{\sqrt {a}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.041 (sec), leaf count = 63
\[y \relax (x ) = \left (c_{1} \left (\sqrt {a}\, x +\sqrt {a \,x^{2}+1}\right )^{\frac {2 i \sqrt {b}}{\sqrt {a}}}+c_{2}\right ) \left (\sqrt {a}\, x +\sqrt {a \,x^{2}+1}\right )^{-\frac {i \sqrt {b}}{\sqrt {a}}}\]