\[ x y'(x)-y(x) f(x y(x))=0 \] ✓ Mathematica : cpu = 19.679 (sec), leaf count = 84
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {f'(K[1] K[2])}{(f(K[1] K[2])+1)^2} \, dK[1]-\frac {1}{K[2] f(x K[2])+K[2]}\right ) \, dK[2]+\int _1^x \frac {f(y(x) K[1])}{K[1] f(y(x) K[1])+K[1]} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.028 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\frac {1}{x}{\it RootOf} \left ( -\ln \left ( x \right ) +{\it \_C1}+\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}\, \left ( 1+f \left ( {\it \_a} \right ) \right ) }}{d{\it \_a}} \right ) } \right \} \]