\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {ay \left ( x \right ) }{ \left ( {x}^{2}+1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.093512 (sec), leaf count = 72 \[ \left \{\left \{y(x)\to c_1 \sqrt {x^2+1} e^{i \sqrt {a+1} \tan ^{-1}(x)}+\frac {i c_2 \sqrt {x^2+1} e^{-i \sqrt {a+1} \tan ^{-1}(x)}}{2 \sqrt {a+1}}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 65 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {{x}^{2}+1} \left ( { \frac {x+i}{-x+i}} \right ) ^{{\frac {1}{2}\sqrt {a+1}}}+{\it \_C2}\, \sqrt {{x}^{2}+1} \left ( {\frac {x+i}{-x+i}} \right ) ^{-{\frac {1}{2} \sqrt {a+1}}} \right \} \]