\[ y''(x)=-\frac {a y(x)}{\left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 0.0863866 (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 = 0.134 (sec), leaf count = 55
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}-1} \left ( \left ( {\frac {x-1}{1+x}} \right ) ^{-{\frac {1}{2}\sqrt {1-a}}}{\it \_C2}+ \left ( {\frac {x-1}{1+x}} \right ) ^{{\frac {1}{2}\sqrt {1-a}}}{\it \_C1} \right ) \right \} \]