\[ y''(x)=\frac {2 x y'(x)}{x^2-1}-\frac {\left (a (a+1)-a (a+3) x^2\right ) y(x)}{x^2 \left (x^2-1\right )} \] ✓ Mathematica : cpu = 0.377332 (sec), leaf count = 38
\[\left \{\left \{y(x)\to c_1 x^{-a}+c_2 \left (-2 a x^2+2 a-x^2+3\right ) x^{a+1}\right \}\right \}\] ✓ Maple : cpu = 0.049 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-a}+{\it \_C2}\, \left ( 2\,a{x}^{2}+{x}^{2}-2\,a-3 \right ) {x}^{a+1} \right \} \]