\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {{b}^{2}y \left ( x \right ) }{ \left ( -{a}^{2}+{x}^{2} \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.323041 (sec), leaf count = 149 \[ \left \{\left \{y(x)\to c_1 (x-a)^{\frac {1}{2} \sqrt {1-\frac {b^2}{a^2}}+\frac {1}{2}} (a+x)^{\frac {1}{2}-\frac {1}{2} \sqrt {1-\frac {b^2}{a^2}}}-\frac {c_2 (x-a)^{\frac {1}{2}-\frac {1}{2} \sqrt {\frac {a^2-b^2}{a^2}}} (a+x)^{\frac {1}{2} \sqrt {\frac {a^2-b^2}{a^2}}+\frac {1}{2}}}{2 a \sqrt {\frac {a^2-b^2}{a^2}}}\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 87 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt { \left ( a-x \right ) \left ( x+a \right ) } \left ( {\frac {a-x}{x+a}} \right ) ^{{\frac {1}{2 \,a}\sqrt {{a}^{2}-{b}^{2}}}}+{\it \_C2}\,\sqrt { \left ( a-x \right ) \left ( x+a \right ) } \left ( {\frac {a-x}{x+a}} \right ) ^{-{\frac {1}{ 2\,a}\sqrt {{a}^{2}-{b}^{2}}}} \right \} \]