\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-1/4\,{\frac { \left ( a{x}^{2}+a-3 \right ) y \left ( x \right ) }{ \left ( {x}^{2}+1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.019002 (sec), leaf count = 78 \[ \left \{\left \{y(x)\to c_1 \sqrt {x^2+1} P_{\frac {1}{2} \left (\sqrt {1-a}-1\right )}^{\frac {1}{2}}(i x)+c_2 \sqrt {x^2+1} Q_{\frac {1}{2} \left (\sqrt {1-a}-1\right )}^{\frac {1}{2}}(i x)\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 61 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt [4]{{x}^{2}+1} \left ( x +\sqrt {{x}^{2}+1} \right ) ^{{\frac {1}{2}\sqrt {1-a}}}+{\it \_C2}\, \sqrt [4]{{x}^{2}+1} \left ( x+\sqrt {{x}^{2}+1} \right ) ^{-{\frac {1}{ 2}\sqrt {1-a}}} \right \} \]