\[ y''(x)=-\frac {a y(x)}{\left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 0.118975 (sec), leaf count = 75
\[\left \{\left \{y(x)\to c_1 \sqrt {1-x^2} e^{-\sqrt {1-a} \tanh ^{-1}(x)}+\frac {c_2 \sqrt {1-x^2} e^{\sqrt {1-a} \tanh ^{-1}(x)}}{2 \sqrt {1-a}}\right \}\right \}\]
✓ Maple : cpu = 0.053 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {{x}^{2}-1} \left ( {\frac {x-1}{1+x}} \right ) ^{{\frac {1}{2}\sqrt {1-a}}}+{\it \_C2}\,\sqrt {{x}^{2}-1} \left ( {\frac {x-1}{1+x}} \right ) ^{-{\frac {1}{2}\sqrt {1-a}}} \right \} \]