\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( y \left ( x \right ) -3/2\,{\frac {{\frac {\rm d}{{\rm d}x}}f \left ( x \right ) }{f \left ( x \right ) }} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{3}-1/2\,{\frac { \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) \left ( y \left ( x \right ) \right ) ^{2}}{f \left ( x \right ) }}+1/2\,{\frac {y \left ( x \right ) }{f \left ( x \right ) } \left ( f \left ( x \right ) +{\frac { \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) ^{2}}{ \left ( f \left ( x \right ) \right ) ^{2}}}-{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left ( x \right ) \right ) }=0} \]
Mathematica: cpu = 0.963122 (sec), leaf count = 82 \[ \text {DSolve}\left [y'(x) \left (y(x)-\frac {3 f'(x)}{2 f(x)}\right )-\frac {y(x)^2 f'(x)}{2 f(x)}+y(x) \left (-\frac {f''(x)}{2 f(x)}+\frac {f'(x)^2}{f(x)^2}+f(x)\right )+y''(x)-y(x)^3=0,y(x),x\right ] \]
Maple: cpu = 0.343 (sec), leaf count = 0 \[ \text {could not solve} \]