\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {{b}^{2}y \left ( x \right ) }{ \left ( {a}^{2}+{x}^{2} \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.236030 (sec), leaf count = 109 \[ \left \{\left \{y(x)\to c_1 \sqrt {a^2+x^2} e^{i \sqrt {\frac {b^2}{a^2}+1} \tan ^{-1}\left (\frac {x}{a}\right )}+\frac {i c_2 \sqrt {a^2+x^2} e^{-i \sqrt {\frac {a^2+b^2}{a^2}} \tan ^{-1}\left (\frac {x}{a}\right )}}{2 a \sqrt {\frac {a^2+b^2}{a^2}}}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 91 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {{a}^{2}+{x}^{2}} \left ( {\frac {ix-a}{ix+a}} \right ) ^{{\frac {1}{2\,a}\sqrt {{a}^{2}+ {b}^{2}}}}+{\it \_C2}\,\sqrt {{a}^{2}+{x}^{2}} \left ( {\frac {ix-a}{ix +a}} \right ) ^{-{\frac {1}{2\,a}\sqrt {{a}^{2}+{b}^{2}}}} \right \} \]