\[ y'(x)=\frac {e^{-x} y(x) \left (x^2 y(x) \log (2 x)-e^x-x \log (2 x)\right )}{x} \] ✓ Mathematica : cpu = 0.0876951 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \frac {2^{e^{-x}}}{x \left (c_1 x^{-e^{-x}} e^{\text {Ei}(-x)}+2^{e^{-x}}\right )}\right \}\right \}\]
✓ Maple : cpu = 0.193 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) =-{\frac {{x}^{{{\rm e}^{-x}}}{2}^{{{\rm e}^{-x}}}{{\rm e}^{{\it Ei} \left ( 1,x \right ) }}}{x \left ( \int \!{x}^{{{\rm e}^{-x}}}{2}^{{{\rm e}^{-x}}}{{\rm e}^{{\it Ei} \left ( 1,x \right ) }}{{\rm e}^{-x}} \left ( \ln \left ( 2 \right ) +\ln \left ( x \right ) \right ) \,{\rm d}x+{\it \_C1} \right ) }} \right \} \]