\[ y'(x)=\frac {x^2 F\left (\frac {y(x)-x \log (x)}{x}\right )+y(x)+x}{x} \] ✓ Mathematica : cpu = 1501.03 (sec), leaf count = 223
\[\text {Solve}\left [\int _1^{y(x)} -\frac {x F\left (\frac {K[2]-x \log (x)}{x}\right ) \int _1^x \left (-\frac {K[2] F'\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )}{K[1]^3 F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )^2}-\frac {F'\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )}{K[1]^2 F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )^2}+\frac {1}{K[1]^2 F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )}\right ) \, dK[1]+1}{x F\left (\frac {K[2]-x \log (x)}{x}\right )} \, dK[2]+\int _1^x \left (\frac {y(x)}{K[1]^2 F\left (\frac {y(x)-K[1] \log (K[1])}{K[1]}\right )}+\frac {1}{K[1] F\left (\frac {y(x)-K[1] \log (K[1])}{K[1]}\right )}+1\right ) \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.108 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) = \left ( \ln \left ( x \right ) +{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right ) x \right \} \]