\[ y''(x)=\frac {a^2 y(x)}{\left (x^2-1\right )^2}-\frac {2 x y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.0196346 (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 = 0.01 (sec), leaf count = 19
\[y \relax (x ) = c_{1} \sinh \left (a \arctanh \relax (x )\right )+c_{2} \cosh \left (a \arctanh \relax (x )\right )\]