\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-\ln \left ( x \right ) +2\,\ln \left ( 2\,x \right ) xy \left ( x \right ) +\ln \left ( 2\,x \right ) +\ln \left ( 2\,x \right ) \left ( y \left ( x \right ) \right ) ^{2}+\ln \left ( 2\,x \right ) {x}^{2}}{\ln \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.265034 (sec), leaf count = 19 \[ \left \{\left \{y(x)\to \tan \left (c_1+\log (2) \text {li}(x)+x\right )-x\right \}\right \} \]
Maple: cpu = 0.561 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) =-x-\tan \left ( \ln \left ( 2 \right ) { \it Ei} \left ( 1,-\ln \left ( x \right ) \right ) +{\it \_C1}-x \right ) \right \} \]