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Differential Equations question

2022 · 29 Jul · Shift 1 · Q31

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JEE Main
Mathematics
Differential Equations
2022 · 29 Jul · Shift 1 · Q31

Differential Equations question

2022 · 29 Jul · Shift 1 · Q31

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let the solution curve

y=y(x)

of the differential equation

\left(1+\mathrm{e}^{2 x}\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}+y\right)=1

pass through the point

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

. Then,

\lim\limits_{x \rightarrow \infty} \mathrm{e}^{x} y(x)

is equal to :

A
$\frac{\pi}{4}$
B
$\frac{3\pi}{4}$
C
$\frac{\pi}{2}$
D
$\frac{3\pi}{2}$

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