\[ y'(x)=\frac {(y(x)+1) (x (y(x)-\log (y(x)+1)-\log (x))+1)}{x y(x)} \] ✓ Mathematica : cpu = 0.154036 (sec), leaf count = 25
DSolve[Derivative[1][y][x] == ((1 + y[x])*(1 + x*(-Log[x] - Log[1 + y[x]] + y[x])))/(x*y[x]),y[x],x]
\[\left \{\left \{y(x)\to -1-W\left (-\frac {e^{-1+c_1 e^x}}{x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.537 (sec), leaf count = 34
dsolve(diff(y(x),x) = (1+y(x))*((y(x)-ln(1+y(x))-ln(x))*x+1)/y(x)/x,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{{\mathrm e}^{x} c_{1}-1}}{x}\right )+{\mathrm e}^{x} c_{1}-1}-x}{x}\]