Let y=y(x) be the solution of the differential equation \cos x (\log _e(\cos x)) ^2 dy + ( \sin x-3 y \sin x \log _e(\cos x)) \dx=0, x \in (0, \frac{\pi}{2}). If y (\frac{\pi}{4}) =\frac{-1}{\log _e 2}, then y (\frac{\pi}{6}) is equal to: [29 Jan 2025 Shift 1]

Correct Answer is : 1loge(3)−loge(4)

\frac{1}{\log _e(3)-\log _e(4)}

\frac{1}{\log _e(4)-\log _e(3)}

\frac{2}{\log _e(3)-\log _e(4)}

JEE Main 29 Jan 2025 Shift 1 Paper

Section: Mathematics

Question : 4 of 75

Marks: +1, -0

Let y=y(x) be the solution of the differential equation
cos‌x(loge(cos‌x))2‌d‌y +(sin‌x−3ysin‌xloge(cos‌x))‌dx=0,‌‌x∈(0,‌

).
If y(‌

)=‌

−1

loge2

, then y(‌

) is equal to:

[29 Jan 2025 Shift 1]

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