\[ y'(x)=\frac {y(x) (x \log (y(x))+\log (y(x))+x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.15342 (sec), leaf count = 22
\[\left \{\left \{y(x)\to x^x (x+1)^{-x} e^{c_1 x}\right \}\right \}\] ✓ Maple : cpu = 0.247 (sec), leaf count = 14
\[y \relax (x ) = \left (\frac {c_{1} x}{1+x}\right )^{x}\]