\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( -{{\rm e}^{x}}+\ln \left ( 2\,x \right ) {x}^{2}y \left ( x \right ) -\ln \left ( 2\,x \right ) x \right ) }{x{{\rm e}^{x}}}}=0} \]
Mathematica: cpu = 0.100013 (sec), leaf count = 49 \[ \left \{\left \{y(x)\to \frac {2^{e^{-x}} x^{e^{-x}-1}}{c_1 e^{\text {Ei}(-x)}+2^{e^{-x}} x^{e^{-x}}}\right \}\right \} \]
Maple: cpu = 0.110 (sec), leaf count = 57 \[ \left \{ y \left ( x \right ) =-{\frac {{x}^{{{\rm e}^{-x}}}{2}^{{ {\rm e}^{-x}}}{{\rm e}^{{\it Ei} \left ( 1,x \right ) }}}{x \left ( \int \!{x}^{{{\rm e}^{-x}}}{2}^{{{\rm e}^{-x}}}{{\rm e}^{{\it Ei} \left ( 1, x \right ) }}{{\rm e}^{-x}} \left ( \ln \left ( 2 \right ) +\ln \left ( x \right ) \right ) \,{\rm d}x+{\it \_C1} \right ) }} \right \} \]