\[ \boxed { \left ( \ln \left ( y \left ( x \right ) \right ) +x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -1=0} \]
Mathematica: cpu = 0.037505 (sec), leaf count = 35 \[ \text {Solve}\left [x=c_1 e^{y(x)}+e^{y(x)} \left (\text {Ei}(-y(x))-e^{-y(x)} \log (y(x))\right ),y(x)\right ] \]
Maple: cpu = 0.046 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -{\it \_Z}- x-{\it Ei} \left ( 1,{{\rm e}^{{\it \_Z}}} \right ) {{\rm e}^{{{\rm e}^{ {\it \_Z}}}}}+{{\rm e}^{{{\rm e}^{{\it \_Z}}}}}{\it \_C1} \right ) }} \right \} \]