\[ 2 a x y'(x)+(a-1) a y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.238582 (sec), leaf count = 87
\[\left \{\left \{y(x)\to \frac {\sqrt {1-x^2} \left (x^2-1\right )^{-a/2} e^{-\sqrt {(a-1)^2} \tanh ^{-1}(x)} \left (c_2 e^{2 \sqrt {(a-1)^2} \tanh ^{-1}(x)}+2 \sqrt {(a-1)^2} c_1\right )}{2 \sqrt {(a-1)^2}}\right \}\right \}\]
✓ Maple : cpu = 0.03 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-1 \right ) ^{1-a}+{\it \_C2}\, \left ( 1+x \right ) ^{1-a} \right \} \]