\[ y''(x)=-\frac {a y(x)}{\left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 0.0937368 (sec), leaf count = 106
\[\left \{\left \{y(x)\to \frac {c_2 \sqrt {1-x^2} (x+1)^{\sqrt {1-a}} (1-x)^{-\sqrt {1-a}} e^{-\sqrt {1-a} \tanh ^{-1}(x)}}{2 \sqrt {1-a}}+c_1 \sqrt {1-x^2} e^{-\sqrt {1-a} \tanh ^{-1}(x)}\right \}\right \}\] ✓ Maple : cpu = 0.053 (sec), leaf count = 55
\[\left \{y \left (x \right ) = \sqrt {x^{2}-1}\, \left (c_{1} \left (\frac {x -1}{x +1}\right )^{\frac {\sqrt {-a +1}}{2}}+c_{2} \left (\frac {x -1}{x +1}\right )^{-\frac {\sqrt {-a +1}}{2}}\right )\right \}\]