\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) -{\frac { \left ( a-1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}{a}}-f \left ( x \right ) \left ( y \left ( x \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{\frac {a \left ( f \left ( x \right ) \right ) ^{2} \left ( y \left ( x \right ) \right ) ^{4}}{ \left ( a+2 \right ) ^{2}}}-{\frac {a \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) \left ( y \left ( x \right ) \right ) ^{3}}{a+2}}=0} \]
Mathematica: cpu = 0.927618 (sec), leaf count = 71 \[ \text {DSolve}\left [-\frac {a y(x)^3 f'(x)}{a+2}+\frac {a f(x)^2 y(x)^4}{(a+2)^2}-\frac {(a-1) y'(x)^2}{a}-f(x) y(x)^2 y'(x)+y(x) y''(x)=0,y(x),x\right ] \]
Maple: cpu = 1.856 (sec), leaf count = 0 \[ \text {could not solve} \]