\[ f(x) \left (y'(x)+y(x)^2\right )-g(x)+y''(x)+2 y(x) y'(x)=0 \] ✗ Mathematica : cpu = 0.137363 (sec), leaf count = 0
, could not solve
DSolve[-g[x] + 2*y[x]*Derivative[1][y][x] + f[x]*(y[x]^2 + Derivative[1][y][x]) + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \textit {\_}b\left (\textit {\_a} \right )\boldsymbol {\mathrm {where}}\left [\left \{\textit {\_}b\left (\textit {\_a} \right )^{2} {\mathrm e}^{\int f \left (\textit {\_a} \right )d \textit {\_a}}+{\mathrm e}^{\int f \left (\textit {\_a} \right )d \textit {\_a}} \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-\left (\int {\mathrm e}^{\int f \left (\textit {\_a} \right )d \textit {\_a}} g \left (\textit {\_a} \right )d \textit {\_a} \right )+c_{1}=0\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=y \relax (x )\right \}, \left \{x =\textit {\_a} , y \relax (x )=\textit {\_}b\left (\textit {\_a} \right )\right \}\right ]\]