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