\[ y'(x)=\frac {x^2 \log (2 x)+2 x y(x) \log (2 x)+y(x)^2 \log (2 x)-\log (x)+\log (2 x)}{\log (x)} \] ✓ Mathematica : cpu = 0.317343 (sec), leaf count = 19
\[\{\{y(x)\to -x+\tan (\log (2) \text {li}(x)+x+c_1)\}\}\] ✓ Maple : cpu = 1.03 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) =-x-\tan \left ( \ln \left ( 2 \right ) {\it Ei} \left ( 1,-\ln \left ( x \right ) \right ) +{\it \_C1}-x \right ) \right \} \]