\[ y''(x)=\frac {a^2 y(x)}{\left (x^2-1\right )^2}-\frac {2 x y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.0224372 (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 = 0.077 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sinh \left ( a{\it Artanh} \left ( x \right ) \right ) +{\it \_C2}\,\cosh \left ( a{\it Artanh} \left ( x \right ) \right ) \right \} \]