Let $$y = y(x)$$ be the solution of the differential equation $$\cos x(\log_{e}(\cos x))^{2}dy + (\sin x-3y\sin x\log_{e}(\cos x))dx=0,x \in (0,\frac{\pi}{2})$$. if $$y\left(\frac{\pi}{4}\right) = \frac{-1}{\log_{e}2}$$, then $$y\left(\frac{\pi}{4}\right)$$ is equal to :

A

$$\frac{1}{\log_{e}(3)-\log_{e}(4)}$$

B

$$\frac{2}{\log_{e}(3)-\log_{e}(4)}$$

C

$$\frac{1}{\log_{e}(4)-\log_{e}(3)}$$

D

$$-\frac{1}{\log_{e}(4)}$$