\[ y'(x)=\frac {(y(x)+1) (x (y(x)-\log (y(x)+1)-\log (x))+1)}{x y(x)} \] ✓ Mathematica : cpu = 0.204835 (sec), leaf count = 25
\[\left \{\left \{y(x)\to -1-W\left (-\frac {e^{-1+c_1 e^x}}{x}\right )\right \}\right \}\] ✓ Maple : cpu = 1.332 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {{\rm e}^{-{\it lambertW} \left ( -{\frac {{{\rm e}^{{{\rm e}^{x}}{\it \_C1}-1}}}{x}} \right ) +{{\rm e}^{x}}{\it \_C1}-1}}-x \right ) } \right \} \]