\[ y'(x)=-\frac {y(x) \cot (x) \left (x^2 y(x) (-\log (2 x))+x \log (2 x)+\tan (x)\right )}{x} \] ✓ Mathematica : cpu = 2.86091 (sec), leaf count = 88
DSolve[Derivative[1][y][x] == -((Cot[x]*y[x]*(x*Log[2*x] + Tan[x] - x^2*Log[2*x]*y[x]))/x),y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\cot (K[1]) K[1] \log (2 K[1])-1}{K[1]}dK[1]\right )}{-\int _1^x\exp \left (\int _1^{K[2]}\frac {-\cot (K[1]) K[1] \log (2 K[1])-1}{K[1]}dK[1]\right ) \cot (K[2]) K[2] \log (2 K[2])dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.326 (sec), leaf count = 75
dsolve(diff(y(x),x) = -y(x)*(tan(x)+ln(2*x)*x-ln(2*x)*x^2*y(x))/x/tan(x),y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\int \frac {-x \ln \left (2\right )-x \ln \left (x \right )-\tan \left (x \right )}{x \tan \left (x \right )}d x}}{\int -\frac {{\mathrm e}^{\int \frac {-x \ln \left (2\right )-x \ln \left (x \right )-\tan \left (x \right )}{x \tan \left (x \right )}d x} \left (\ln \left (2\right )+\ln \left (x \right )\right ) x}{\tan \left (x \right )}d x +c_{1}}\]