\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left ( x \right ) \right ) y \left ( x \right ) +f \left ( x \right ) \left ( y \left ( x \right ) \right ) ^{3}- \left ( y \left ( x \right ) \right ) ^{4}=0} \]
Mathematica: cpu = 0.482561 (sec), leaf count = 52 \[ \text {DSolve}\left [-y(x) f''(x)+f'(x) y'(x)+f(x) y(x)^3+y(x) y''(x)-y'(x)^2-y(x)^4=0,y(x),x\right ] \]
Maple: cpu = 0.390 (sec), leaf count = 0 \[ \text {could not solve} \]