\[ 2 a x y'(x)+(a-1) a y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.229094 (sec), leaf count = 97
\[\left \{\left \{y(x)\to c_1 \sqrt {1-x^2} \left (x^2-1\right )^{-a/2} e^{-\sqrt {(a-1)^2} \tanh ^{-1}(x)}+\frac {c_2 \sqrt {1-x^2} \left (x^2-1\right )^{-a/2} e^{\sqrt {(a-1)^2} \tanh ^{-1}(x)}}{2 \sqrt {(a-1)^2}}\right \}\right \}\] ✓ Maple : cpu = 0.03 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( 1+x \right ) ^{1-a}+{\it \_C2}\, \left ( x-1 \right ) ^{1-a} \right \} \]