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Differential Equations question

2024 · 31 Jan · Shift 1 · Q37

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JEE Main
Mathematics
Differential Equations
2024 · 31 Jan · Shift 1 · Q37

Differential Equations question

2024 · 31 Jan · Shift 1 · Q37

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y=y(x)

be the solution of the differential equation

\frac{d y}{d x}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x \tan x)}, x \in\left(0, \frac{\pi}{2}\right)

satisfying the condition

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

. Then,

y\left(\frac{\pi}{3}\right)

is

A
$\sqrt{3}\left(2+\log _e 3\right)$
B
$\sqrt{3}\left(1+2 \log _e 3\right)$
C
$\sqrt{3}\left(2+\log _e \sqrt{3}\right)$
D
$\frac{\sqrt{3}}{2}\left(2+\log _e 3\right)$

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