\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =2\,{\frac {x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{2}-1}}-{\frac { \left ( a \left ( a+1 \right ) -a{x}^{2} \left ( a+3 \right ) \right ) y \left ( x \right ) }{{x}^{2} \left ( {x}^{2}-1 \right ) }}=0} \]
Mathematica: cpu = 0.471560 (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 = 0.015 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-a}+{\it \_C2}\,{x}^{a+1 } \left ( 2\,a{x}^{2}+{x}^{2}-2\,a-3 \right ) \right \} \]