\[ 2 a x y'(x)+(a-1) a y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.166144 (sec), leaf count = 128
\[\left \{\left \{y(x)\to \frac {c_2 \sqrt {1-x^2} (x+1)^{\sqrt {(a-1)^2}} \left (x^2-1\right )^{-a/2} (1-x)^{-\sqrt {(a-1)^2}} e^{-\sqrt {(a-1)^2} \tanh ^{-1}(x)}}{2 \sqrt {(a-1)^2}}+c_1 \sqrt {1-x^2} \left (x^2-1\right )^{-a/2} e^{-\sqrt {(a-1)^2} \tanh ^{-1}(x)}\right \}\right \}\] ✓ Maple : cpu = 0.063 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-1 \right ) ^{1-a}+{\it \_C2}\, \left ( 1+x \right ) ^{1-a} \right \} \]