\[ y'(x)=\frac {e^{-x} y(x) \left (x^2 y(x) \log (2 x)-e^x-x \log (2 x)\right )}{x} \] ✓ Mathematica : cpu = 0.364543 (sec), leaf count = 49
\[\left \{\left \{y(x)\to \frac {2^{e^{-x}} x^{e^{-x}-1}}{2^{e^{-x}} x^{e^{-x}}+c_1 e^{\text {Ei}(-x)}}\right \}\right \}\] ✓ Maple : cpu = 0.338 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) = \left ( {2}^{-{{\rm e}^{-x}}}{x}^{-{{\rm e}^{-x}}+1}{\it \_C1}\,{{\rm e}^{-{\it Ei} \left ( 1,x \right ) }}+x \right ) ^{-1} \right \} \]