\[ a x y'(x)+(a-2) y(x)+\left (x^2+1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0203666 (sec), leaf count = 82
\[\left \{\left \{y(x)\to c_1 \left (x^2+1\right )^{\frac {2-a}{4}} P_{\frac {a-4}{2}}^{\frac {a-2}{2}}(i x)+c_2 \left (x^2+1\right )^{\frac {2-a}{4}} Q_{\frac {a-4}{2}}^{\frac {a-2}{2}}(i x)\right \}\right \}\] ✓ Maple : cpu = 0.214 (sec), leaf count = 36
\[\left \{y \left (x \right ) = c_{2} x \hypergeom \left (\left [1, \frac {a}{2}-\frac {1}{2}\right ], \left [\frac {3}{2}\right ], -x^{2}\right )+c_{1} \left (x^{2}+1\right )^{-\frac {a}{2}+1}\right \}\]