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Differential Equations question

2022 · 28 Jul · Shift 1 · Q31

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JEE Main
Mathematics
Differential Equations
2022 · 28 Jul · Shift 1 · Q31

Differential Equations question

2022 · 28 Jul · Shift 1 · Q31

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If

y=y(x), x \in(0, \pi / 2)

be the solution curve of the differential equation

\left(\sin ^{2} 2 x\right) \frac{d y}{d x}+\left(8 \sin ^{2} 2 x+2 \sin 4 x\right) y=2 \mathrm{e}^{-4 x}(2 \sin 2 x+\cos 2 x)

, with

y(\pi / 4)=\mathrm{e}^{-\pi}

, then

y(\pi / 6)

is equal to :

A
$\frac{2}{\sqrt{3}} e^{-2 \pi / 3}$
B
$\frac{2}{\sqrt{3}} \mathrm{e}^{2 \pi / 3}$
C
$\frac{1}{\sqrt{3}} e^{-2 \pi / 3}$
D
$\frac{1}{\sqrt{3}} e^{2 \pi / 3}$

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