\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a \left ( a-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.224528 (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 = 0.031 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( 1+x \right ) ^{1-a}+{ \it \_C2}\, \left ( x-1 \right ) ^{1-a} \right \} \]