\[ -\frac {a^2 y(x) f'(x)^2}{b^2+f(x)^2}+\frac {f(x) f^3(x) y'(x)}{b^2+f(x)^2}+y''(x)=0 \] ✗ Mathematica : cpu = 0.667839 (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 or ODESolStruc
\[y \relax (x ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \relax (x )+\frac {f \relax (x ) \left (\frac {d^{3}}{d x^{3}}f \relax (x )\right ) \left (\frac {d}{d x}\textit {\_Y} \relax (x )\right )}{f \relax (x )^{2}+b^{2}}-\frac {a^{2} \left (\frac {d}{d x}f \relax (x )\right )^{2} \textit {\_Y} \relax (x )}{f \relax (x )^{2}+b^{2}}\right \}, \left \{\textit {\_Y} \relax (x )\right \}\right )\]