\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\,y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{3}+f \left ( x \right ) y \left ( x \right ) -g \left ( x \right ) =0} \]
Mathematica: cpu = 7.278424 (sec), leaf count = 32 \[ \text {DSolve}\left [f(x) y(x)-g(x)+y''(x)+3 y(x) y'(x)+y(x)^3=0,y(x),x\right ] \]
Maple: cpu = 0.0 (sec), leaf count = 63 \[ \left \{ y \left ( x \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}{\it DESol} \left ( \left \{ -g \left ( x \right ) {\it \_Y} \left ( x \right ) +f \left ( x \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) +{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) }{{\it DESol} \left ( \left \{ -g \left ( x \right ) {\it \_Y} \left ( x \right ) +f \left ( x \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) +{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) }} \right \} \]