\[ y'(x)=\frac {x^2 F\left (\frac {y(x)-x \log (x)}{x}\right )+y(x)+x}{x} \] ✓ Mathematica : cpu = 0.310001 (sec), leaf count = 226
DSolve[Derivative[1][y][x] == (x + x^2*F[(-(x*Log[x]) + y[x])/x] + y[x])/x,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {x F\left (\frac {K[2]-x \log (x)}{x}\right ) \int _1^x\left (-\frac {K[2] F'\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )}{F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )^2 K[1]^3}-\frac {F'\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )}{F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right )^2 K[1]^2}+\frac {1}{F\left (\frac {K[2]-K[1] \log (K[1])}{K[1]}\right ) K[1]^2}\right )dK[1]+1}{x F\left (\frac {K[2]-x \log (x)}{x}\right )}dK[2]+\int _1^x\left (\frac {y(x)}{F\left (\frac {y(x)-K[1] \log (K[1])}{K[1]}\right ) K[1]^2}+\frac {1}{F\left (\frac {y(x)-K[1] \log (K[1])}{K[1]}\right ) K[1]}+1\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.109 (sec), leaf count = 23
dsolve(diff(y(x),x) = (x+y(x)+F(-(-y(x)+x*ln(x))/x)*x^2)/x,y(x))
\[y \left (x \right ) = \left (\ln \left (x \right )+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right )\right ) x\]