\[ -y(x) \left (g'(x)-y(x)^2 f'(x)\right )+y'(x) \left (f(x) y(x)^2+g(x)\right )+y(x) y''(x)-y'(x)^2=0 \] ✗ Mathematica : cpu = 20.8017 (sec), leaf count = 0
, could not solve
DSolve[-(y[x]*(-(y[x]^2*Derivative[1][f][x]) + Derivative[1][g][x])) + (g[x] + f[x]*y[x]^2)*Derivative[1][y][x] - Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \textit {\_}b\left (\textit {\_a} \right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )}{\textit {\_}b\left (\textit {\_a} \right )}-\frac {-f \left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )^{2}-c_{1} \textit {\_}b\left (\textit {\_a} \right )+g \left (\textit {\_a} \right )}{\textit {\_}b\left (\textit {\_a} \right )}=0\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=y \relax (x )\right \}, \left \{x =\textit {\_a} , y \relax (x )=\textit {\_}b\left (\textit {\_a} \right )\right \}\right ]\]