\[ y'(x)=(1-y(x)) \left (-f(x)+\frac {y(x) \log (y(x)-1)}{x (1-y(x)) \log (x)}-\frac {\log (y(x)-1)}{x (1-y(x)) \log (x)}\right ) \] ✓ Mathematica : cpu = 320.617 (sec), leaf count = 84
\[\text {Solve}\left [\int _1^x \left (-\frac {f(K[1])}{\log (K[1])}-\frac {\log (y(x)-1)}{K[1] \log ^2(K[1])}\right ) \, dK[1]+\int _1^{y(x)} \left (\frac {1}{\log (x) (K[2]-1)}-\int _1^x -\frac {1}{K[1] (K[2]-1) \log ^2(K[1])} \, dK[1]\right ) \, dK[2]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.342 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\int \!{\frac {f \left ( x \right ) }{\ln \left ( x \right ) }}\,{\rm d}x\ln \left ( x \right ) }}{x}^{{\it \_C1}}+1 \right \} \]