\[ \boxed { 2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+4\, \left ( y \left ( x \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +1+f \left ( x \right ) \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4}=0} \]
Mathematica: cpu = 0.050506 (sec), leaf count = 45 \[ \text {DSolve}\left [f(x) y(x)^2+2 y(x) y''(x)+4 y(x)^2 y'(x)-y'(x)^2+y(x)^4+1=0,y(x),x\right ] \]
Maple: cpu = 0.265 (sec), leaf count = 0 \[ \text {could not solve} \]