\[ y'(x)=\frac {y(x)^2 F\left (\frac {1-y(x) \log (x)}{y(x)}\right )}{x} \] ✓ Mathematica : cpu = 0.250712 (sec), leaf count = 245
DSolve[Derivative[1][y][x] == (F[(1 - Log[x]*y[x])/y[x]]*y[x]^2)/x,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{\left (-F\left (\frac {1-K[2] \log (x)}{K[2]}\right )-1\right ) K[2]^2}-\int _1^x\left (\frac {\left (-\frac {\log (K[1])}{K[2]}-\frac {1-K[2] \log (K[1])}{K[2]^2}\right ) F'\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )}{\left (F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )+1\right ) K[1]}-\frac {F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right ) \left (-\frac {\log (K[1])}{K[2]}-\frac {1-K[2] \log (K[1])}{K[2]^2}\right ) F'\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )}{\left (F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )+1\right )^2 K[1]}\right )dK[1]\right )dK[2]+\int _1^x\frac {F\left (\frac {1-\log (K[1]) y(x)}{y(x)}\right )}{\left (F\left (\frac {1-\log (K[1]) y(x)}{y(x)}\right )+1\right ) K[1]}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.167 (sec), leaf count = 38
dsolve(diff(y(x),x) = F(-(-1+y(x)*ln(x))/y(x))*y(x)^2/x,y(x))
\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{\left (F \left (\frac {1-\textit {\_a} \ln \left (x \right )}{\textit {\_a}}\right )+1\right ) \textit {\_a}^{2}}d \textit {\_a} -\ln \left (x \right )-c_{1} = 0\]