\[ y''(x)=\frac {2 x y'(x)}{x^2-1}-\frac {\left (a (a+1)-a (a+3) x^2\right ) y(x)}{x^2 \left (x^2-1\right )} \] ✓ Mathematica : cpu = 0.330668 (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 = 0.033 (sec), leaf count = 33
\[y \relax (x ) = c_{1} x^{-a}+c_{2} x^{a +1} \left (2 a \,x^{2}+x^{2}-2 a -3\right )\]