\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +f \left ( x \right ) \left ( y \left ( x \right ) \right ) ^{3}+ \left ( y \left ( x \right ) \right ) ^{2} \left ( {\frac {{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left ( x \right ) }{f \left ( x \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) ^{2}}{ \left ( f \left ( x \right ) \right ) ^{2}}} \right ) =0} \]
Mathematica: cpu = 41.261240 (sec), leaf count = 62 \[ \text {DSolve}\left [y(x)^2 \left (\frac {f''(x)}{f(x)}-\frac {f'(x)^2}{f(x)^2}\right )+f(x) y(x)^3+y(x) y''(x)-y'(x)^2-y'(x)=0,y(x),x\right ] \]
Maple: cpu = 0.390 (sec), leaf count = 0 \[ \text {could not solve} \]