\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-2\,{\frac {x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{2}-1}}+{\frac {{a}^{2}y \left ( x \right ) }{ \left ( {x}^{2}-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.028504 (sec), leaf count = 53 \[ \left \{\left \{y(x)\to c_1 \cosh \left (\frac {1}{2} a (\log (1-x)-\log (x+1))\right )+i c_2 \sinh \left (\frac {1}{2} a (\log (1-x)-\log (x+1))\right )\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 19 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sinh \left ( a{\it Artanh} \left ( x \right ) \right ) +{\it \_C2}\,\cosh \left ( a{\it Artanh} \left ( x \right ) \right ) \right \} \]