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 (0, (π)/2). If y((π)/4) = (-1)/(log e 2), then y((π)/6) is equal to:

Differential Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q118

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumDifferential Equations163× since 2002

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 \left(0, \frac{\pi}{2}\right)

. If

y\left(\frac{\pi}{4}\right) = \frac{-1}{\log_e 2}

, then

y\left(\frac{\pi}{6}\right)

is equal to: