Let \(y = y(x)\) be the solution of the differential equation \(\cos x{\left({\log }_{e}(\cos x)\right)}^{2}dy\)\(+\left…

Let \(y = y(x)\) be the solution of the differential equation \(\cos x{\left({\log }_{e}(\cos x)\right)}^{2}dy\)\(+\left(\sin x-3y\sin x{\log }_{e}(\cos x)\right)dx=0\), \(\mathrm{x}\in \left(0,\frac{\pi }{2}\right)\text{. If }\mathrm{y}\left(\frac{\pi }{4}\right)=\frac{-1}{{\log }_{\mathrm{e}}2}\text{, then }\mathrm{y}\left(\frac{\pi }{6}\right)\) is:

[JEE Main 2025, 29 Jan (Shift 1)]