\[ a y(x)+\left (x^2-1\right ) y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.0665848 (sec), leaf count = 97
\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {1}{2} \sqrt {a} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )\right )\right )-c_2 \sin \left (\frac {1}{2} \sqrt {a} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.037 (sec), leaf count = 45
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C1}\, \left ( \left ( x+\sqrt {{x}^{2}-1} \right ) ^{i\sqrt {a}} \right ) ^{2}+{\it \_C2} \right ) \left ( \left ( x+\sqrt {{x}^{2}-1} \right ) ^{i\sqrt {a}} \right ) ^{-1}} \right \} \]