\[ y'(x)=\frac {x^3+2 x^2 y(x)-x y(x)-y(x)^2+x y(x) \log (x)}{x^2 (x+\log (x))} \] ✓ Mathematica : cpu = 0.933371 (sec), leaf count = 351
DSolve[Derivative[1][y][x] == (x^3 - x*y[x] + 2*x^2*y[x] + x*Log[x]*y[x] - y[x]^2)/(x^2*(x + Log[x])),y[x],x]
\[\left \{\left \{y(x)\to \frac {x^2 (x+\log (x)) \left (-\frac {\sqrt {x} (x+\log (x)+2) \log (x) \exp \left (-\frac {1}{2} \int _1^x\frac {K[5]+\log (K[5])+2}{K[5]^2+\log (K[5]) K[5]}dK[5]\right )}{2 \left (x^2+x \log (x)\right )}+c_1 \left (\frac {\exp \left (-\frac {1}{2} \int _1^x\frac {K[5]+\log (K[5])+2}{K[5]^2+\log (K[5]) K[5]}dK[5]\right )}{2 \sqrt {x}}-\frac {\sqrt {x} (x+\log (x)+2) \exp \left (-\frac {1}{2} \int _1^x\frac {K[5]+\log (K[5])+2}{K[5]^2+\log (K[5]) K[5]}dK[5]\right )}{2 \left (x^2+x \log (x)\right )}\right )+\frac {\log (x) \exp \left (-\frac {1}{2} \int _1^x\frac {K[5]+\log (K[5])+2}{K[5]^2+\log (K[5]) K[5]}dK[5]\right )}{2 \sqrt {x}}+\frac {\exp \left (-\frac {1}{2} \int _1^x\frac {K[5]+\log (K[5])+2}{K[5]^2+\log (K[5]) K[5]}dK[5]\right )}{\sqrt {x}}\right )}{\sqrt {x} \log (x) \exp \left (-\frac {1}{2} \int _1^x\frac {K[5]+\log (K[5])+2}{K[5]^2+\log (K[5]) K[5]}dK[5]\right )+c_1 \sqrt {x} \exp \left (-\frac {1}{2} \int _1^x\frac {K[5]+\log (K[5])+2}{K[5]^2+\log (K[5]) K[5]}dK[5]\right )}\right \}\right \}\] ✓ Maple : cpu = 0.127 (sec), leaf count = 19
dsolve(diff(y(x),x) = 1/x^2*(2*x^2*y(x)+x^3+y(x)*ln(x)*x-y(x)^2-x*y(x))/(x+ln(x)),y(x))
\[y \left (x \right ) = \frac {x \left (c_{1} x -1\right )}{c_{1} \ln \left (x \right )+1}\]