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Differential Equations question

2025 · 29 Jan · Shift 1 · Q36

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JEE Main
Mathematics
Differential Equations
2025 · 29 Jan · Shift 1 · Q36

Differential Equations question

2025 · 29 Jan · Shift 1 · Q36

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

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 :

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

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