\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( g \left ( x \right ) +f \left ( x \right ) \left ( y \left ( x \right ) \right ) ^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}g \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) \left ( y \left ( x \right ) \right ) ^{2} \right ) =0} \]
Mathematica: cpu = 21.002667 (sec), leaf count = 56 \[ \text {DSolve}\left [-y(x) \left (g'(x)-y(x)^2 f'(x)\right )+y'(x) \left (f(x) y(x)^2+g(x)\right )+y(x) y''(x)-y'(x)^2=0,y(x),x\right ] \]
Maple: cpu = 0.234 (sec), leaf count = 60 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ {\frac {{\frac {\rm d}{{\rm d}{ \it \_a}}}{\it \_b} \left ( {\it \_a} \right ) }{{\it \_b} \left ( {\it \_a} \right ) }}+{\frac {f \left ( {\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_C1}\,{\it \_b} \left ( { \it \_a} \right ) -g \left ( {\it \_a} \right ) }{{\it \_b} \left ( {\it \_a} \right ) }}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( { \it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \]