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