\[ f(x) \left (y'(x)+y(x)^2\right )-g(x)+y''(x)+2 y(x) y'(x)=0 \] ✗ Mathematica : cpu = 0.159211 (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 = 0.889 (sec), leaf count = 58
\[\{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_}b\left (\textit {\_a} \right ), \left [\left \{c_{1}-\left (\int {\mathrm e}^{\int f \left (\textit {\_a} \right )d \textit {\_a}} g \left (\textit {\_a} \right )d \textit {\_a} \right )+\left (\textit {\_}b\left (\textit {\_a} \right )^{2}+\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right ) {\mathrm e}^{\int f \left (\textit {\_a} \right )d \textit {\_a}}=0\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=y \left (x \right )\right \}, \left \{x =\textit {\_a} , y \left (x \right )=\textit {\_}b\left (\textit {\_a} \right )\right \}\right ]\right )\}\]