\[ \boxed { \left ( {x}^{2}+1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.014502 (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 = 0.047 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={{\it \_C1} \left ( x+\sqrt {{x}^{2}+1} \right ) ^{\sqrt {1-a}}{\frac {1}{\sqrt {{x}^{2}+1}}}}+{{\it \_C2} \left ( x+\sqrt {{x}^{2}+1} \right ) ^{-\sqrt {1-a}}{\frac {1}{\sqrt {{ x}^{2}+1}}}} \right \} \]