Let \( y=y(x) \) be the solution of the differentiable equation \( \cos x\, (3\sin x+\cos x+3)\,dy=(1+y\sin x\,(3\sin x+\cos x+3))\,dx, \; 0\le x\le \dfrac{\pi}{2}, \; y(0)=0 \). Then, \( y\!\left(\dfrac{\pi}{3}\right) \) is equal to:
\( 2\log_{e}\!\left(\dfrac{3\sqrt{3}-8}{4}\right) \)
\( 2\log_{e}\!\left(\dfrac{\sqrt{3}+7}{2}\right) \)
\( 2\log_{e}\!\left(\dfrac{2\sqrt{3}+10}{11}\right) \)
\( 2\log_{e}\!\left(\dfrac{2\sqrt{3}+9}{6}\right) \)
