JEE Math Practice Question

Let y = y(x) be the solution of the differential equation : $\cos x\left(\log _e(\cos x)\right)^2 d y+\left(\sin x-3 y \sin x \log _e(\cos x)\right) d x=0$, x ∈ (0, $\frac{\pi}{2}$ ). If $ y(\frac{\pi}{4}) $ = $-\frac{1}{\log_{e}2}$, then $ y(\frac{\pi}{6}) $ is equal to :

1. A.$\frac{2}{\log_{e}(3)−\log_{e}(4)}$
2. B.$-\frac{1}{\log_{e}(4)}$
3. C.$\frac{1}{\log_{e}(4)−\log_{e}(3)}$
4. D.$\frac{1}{\log_{e}(3)−\log_{e}(4)}$