\[ y'(x)=\frac {x^2 F\left (\frac {y(x)-x \log (x)}{x}\right )+y(x)+x}{x} \] ✓ Mathematica : cpu = 0.349883 (sec), leaf count = 226
\[\text {Solve}\left [\int _1^{y(x)}-\frac {x F\left (\frac {K[2]-x \log (x)}{x}\right ) \int _1^x\left (-\frac {K[2] F'\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )}{F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )^2 K[1]^3}-\frac {F'\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )}{F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )^2 K[1]^2}+\frac {1}{F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right ) K[1]^2}\right )dK[1]+1}{x F\left (\frac {K[2]-x \log (x)}{x}\right )}dK[2]+\int _1^x\left (\frac {y(x)}{F\left (\frac {y(x)-K[1] \log (K[1])}{K[1]}\right ) K[1]^2}+\frac {1}{F\left (\frac {y(x)-K[1] \log (K[1])}{K[1]}\right ) K[1]}+1\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.105 (sec), leaf count = 23
\[\left \{y \left (x \right ) = \left (\RootOf \left (c_{1}-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+\ln \left (x \right )\right ) x\right \}\]