\[ x y'(x)-y(x) f(x y(x))=0 \] ✓ Mathematica : cpu = 0.155067 (sec), leaf count = 115
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{(-f(x K[2])-1) K[2]}-\int _1^x\left (\frac {f'(K[1] K[2])}{f(K[1] K[2])+1}-\frac {f(K[1] K[2]) f'(K[1] K[2])}{(f(K[1] K[2])+1)^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {f(K[1] y(x))}{(f(K[1] y(x))+1) K[1]}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.018 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\frac {1}{x}{\it RootOf} \left ( -\ln \left ( x \right ) +{\it \_C1}+\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}\, \left ( 1+f \left ( {\it \_a} \right ) \right ) }}{d{\it \_a}} \right ) } \right \} \]