\[ -\frac {a^2 y(x) f'(x)^2}{b^2+f(x)^2}+\frac {f(x) f^3(x) y'(x)}{b^2+f(x)^2}+y''(x)=0 \] ✗ Mathematica : cpu = 0.716785 (sec), leaf count = 0 , could not solve
DSolve[-((a^2*y[x]*Derivative[1][f][x]^2)/(b^2 + f[x]^2)) + (f[x]*(f^3)[x]*Derivative[1][y][x])/(b^2 + f[x]^2) + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac {f \left ( x \right ) \left ( {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{ \left ( f \left ( x \right ) \right ) ^{2}+{b}^{2}}}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) ^{2}{a}^{2}{\it \_Y} \left ( x \right ) }{ \left ( f \left ( x \right ) \right ) ^{2}+{b}^{2}}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]