\[ -\frac {a^2 y(x) f'(x)^2}{b^2+f(x)^2}+\frac {f(x) f^3(x) y'(x)}{b^2+f(x)^2}+y''(x)=0 \] ✗ Mathematica : cpu = 0.667839 (sec), leaf count = 0
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]
, 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
dsolve(diff(diff(y(x),x),x)+f(x)*diff(diff(diff(f(x),x),x),x)/(f(x)^2+b^2)*diff(y(x),x)-a^2*diff(f(x),x)^2/(f(x)^2+b^2)*y(x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )+\frac {f \left (x \right ) \left (\frac {d^{3}}{d x^{3}}f \left (x \right )\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{f \left (x \right )^{2}+b^{2}}-\frac {a^{2} \left (\frac {d}{d x}f \left (x \right )\right )^{2} \textit {\_Y} \left (x \right )}{f \left (x \right )^{2}+b^{2}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]