\[ y'(x)=-\frac {y(x) \cot (x) \left (x^2 y(x) (-\log (2 x))+x \log (2 x)+\tan (x)\right )}{x} \] ✓ Mathematica : cpu = 3.21904 (sec), leaf count = 88
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\cot (K[1]) K[1] \log (2 K[1])-1}{K[1]}dK[1]\right )}{-\int _1^x\exp \left (\int _1^{K[2]}\frac {-\cot (K[1]) K[1] \log (2 K[1])-1}{K[1]}dK[1]\right ) \cot (K[2]) K[2] \log (2 K[2])dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.31 (sec), leaf count = 75
\[\left \{y \left (x \right ) = \frac {{\mathrm e}^{\int \frac {-x \ln \left (x \right )-\ln \left (2\right ) x -\tan \left (x \right )}{x \tan \left (x \right )}d x}}{c_{1}+\int -\frac {\left (\ln \left (x \right )+\ln \left (2\right )\right ) x \,{\mathrm e}^{\int \frac {-x \ln \left (x \right )-\ln \left (2\right ) x -\tan \left (x \right )}{x \tan \left (x \right )}d x}}{\tan \left (x \right )}d x}\right \}\]