\[ f(x) \left (y'(x)+y(x)^2\right )-g(x)+y''(x)+2 y(x) y'(x)=0 \] ✗ Mathematica : cpu = 0.306068 (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 = 1.198 (sec), leaf count = 58
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ -\int \!{{\rm e}^{\int \!f \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}}}g \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+ \left ( \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {{\rm e}^{\int \!f \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}}}+{\it \_C1}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \]