\[ y'(x)=(1-y(x)) \left (-f(x)+\frac {y(x) \log (y(x)-1)}{x (1-y(x)) \log (x)}-\frac {\log (y(x)-1)}{x (1-y(x)) \log (x)}\right ) \] ✓ Mathematica : cpu = 0.333367 (sec), leaf count = 87
\[\text {Solve}\left [\int _1^x\left (-\frac {f(K[1])}{\log (K[1])}-\frac {\log (y(x)-1)}{K[1] \log ^2(K[1])}\right )dK[1]+\int _1^{y(x)}\left (\frac {1}{(K[2]-1) \log (x)}-\int _1^x-\frac {1}{K[1] (K[2]-1) \log ^2(K[1])}dK[1]\right )dK[2]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.184 (sec), leaf count = 23
\[y \relax (x ) = {\mathrm e}^{\left (\int \frac {f \relax (x )}{\ln \relax (x )}d x \right ) \ln \relax (x )} x^{c_{1}}+1\]