\[ y'(x)=\frac {(y(x)+1) (x (y(x)-\log (y(x)+1)-\log (x))+1)}{x y(x)} \] ✓ Mathematica : cpu = 0.096942 (sec), leaf count = 25
\[\left \{\left \{y(x)\to -W\left (-\frac {e^{c_1 e^x-1}}{x}\right )-1\right \}\right \}\]
✓ Maple : cpu = 0.496 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {{\rm e}^{-{\it lambertW} \left ( -{\frac {{{\rm e}^{{\it \_C1}\,{{\rm e}^{x}}-1}}}{x}} \right ) +{\it \_C1}\,{{\rm e}^{x}}-1}}-x \right ) } \right \} \]