\[ -y(x) \left (g'(x)-y(x)^2 f'(x)\right )+y'(x) \left (f(x) y(x)^2+g(x)\right )-y'(x)^2+y(x) y''(x)=0 \] ✗ Mathematica : cpu = 20.7906 (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 = 0.546 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ {\frac {f \left ( {\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_b} \left ( {\it \_a} \right ) {\it \_C1}+{\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) -g \left ( {\it \_a} \right ) }{{\it \_b} \left ( {\it \_a} \right ) }}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \]