\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {ay \left ( x \right ) }{ \left ( {x}^{2}-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.102513 (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 = 0.031 (sec), leaf count = 61 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {{x}^{2}-1} \left ( { \frac {x-1}{1+x}} \right ) ^{{\frac {1}{2}\sqrt {1-a}}}+{\it \_C2}\, \sqrt {{x}^{2}-1} \left ( {\frac {x-1}{1+x}} \right ) ^{-{\frac {1}{2} \sqrt {1-a}}} \right \} \]