\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.026503 (sec), leaf count = 50 \[ \left \{\left \{y(x)\to c_2 \sin \left (\sqrt {a} \log \left (\sqrt {x^2-1}+x\right )\right )+c_1 \cos \left (\sqrt {a} \log \left (\sqrt {x^2-1}+x\right )\right )\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x+\sqrt {{x}^{2}-1} \right ) ^{i\sqrt {a}}+{{\it \_C2} \left ( \left ( x+\sqrt {{x}^{2}-1} \right ) ^{i\sqrt {a}} \right ) ^{-1}} \right \} \]