\[ a y(x)+\left (x^2+1\right ) y''(x)+3 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0121589 (sec), leaf count = 82
\[\left \{\left \{y(x)\to \frac {c_1 P_{\frac {1}{2} \left (2 \sqrt {1-a}-1\right )}^{\frac {1}{2}}(i x)}{\sqrt [4]{x^2+1}}+\frac {c_2 Q_{\frac {1}{2} \left (2 \sqrt {1-a}-1\right )}^{\frac {1}{2}}(i x)}{\sqrt [4]{x^2+1}}\right \}\right \}\] ✓ Maple : cpu = 0.446 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={ \left ( {\it \_C2}\, \left ( x+\sqrt {{x}^{2}+1} \right ) ^{-\sqrt {1-a}}+{\it \_C1}\, \left ( x+\sqrt {{x}^{2}+1} \right ) ^{\sqrt {1-a}} \right ) {\frac {1}{\sqrt {{x}^{2}+1}}}} \right \} \]