\[ \boxed { \left ( 1+x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) \left ( y \left ( x \right ) -x \right ) =0} \]
Mathematica: cpu = 0.027504 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to -\frac {e^{x+1}}{-e c_1 x-e c_1-x \text {Ei}(x+1)-\text {Ei}(x+1)+e^{x+1}}\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) =-{\frac {{{\rm e}^{x}}}{{{\rm e}^{-1}}{ \it Ei} \left ( 1,-1-x \right ) x+{{\rm e}^{-1}}{\it Ei} \left ( 1,-1-x \right ) -{\it \_C1}\,x+{{\rm e}^{x}}-{\it \_C1}}} \right \} \]