\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac {f \left ( x \right ) \left ( {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( f \left ( x \right ) \right ) ^{2}+{b}^{2}}}-{\frac {{a}^{2} \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) ^{2}y \left ( x \right ) }{ \left ( f \left ( x \right ) \right ) ^{2}+{b}^{2}}}=0} \]
Mathematica: cpu = 0.810103 (sec), leaf count = 55 \[ \text {DSolve}\left [-\frac {a^2 y(x) f'(x)^2}{b^2+f(x)^2}+\frac {f(x) f^3(x) y'(x)}{b^2+f(x)^2}+y''(x)=0,y(x),x\right ] \]
Maple: cpu = 0.561 (sec), leaf count = 64 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac {f \left ( x \right ) \left ( {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{ \left ( f \left ( x \right ) \right ) ^{2}+{b}^{2}}}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) ^{2}{a}^{ 2}{\it \_Y} \left ( x \right ) }{ \left ( f \left ( x \right ) \right ) ^{2 }+{b}^{2}}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]