\[ a y(x)+\left (x^2+1\right ) y''(x)+3 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0169537 (sec), leaf count = 66
\[\left \{\left \{y(x)\to \frac {c_1 P_{\sqrt {1-a}-\frac {1}{2}}^{\frac {1}{2}}(i x)+c_2 Q_{\sqrt {1-a}-\frac {1}{2}}^{\frac {1}{2}}(i x)}{\sqrt [4]{x^2+1}}\right \}\right \}\]
✓ Maple : cpu = 0.188 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C2}\, \left ( x+\sqrt {{x}^{2}+1} \right ) ^{-\sqrt {1-a}}+{\it \_C1}\, \left ( x+\sqrt {{x}^{2}+1} \right ) ^{\sqrt {1-a}} \right ) {\frac {1}{\sqrt {{x}^{2}+1}}}} \right \} \]