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Differential Equations question

2022 · 25 Jul · Shift 1 · Q30

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JEE Main
Mathematics
Differential Equations
2022 · 25 Jul · Shift 1 · Q30

Differential Equations question

2022 · 25 Jul · Shift 1 · Q30

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

The slope of the tangent to a curve

C: y=y(x)

at any point

(x, y)

on it is

\frac{2 \mathrm{e}^{2 x}-6 \mathrm{e}^{-x}+9}{2+9 \mathrm{e}^{-2 x}}

. If

C

passes through the points

\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right)

and

\left(\alpha, \frac{1}{2} \mathrm{e}^{2 \alpha}\right)

, then

\mathrm{e}^{\alpha}

is equal to :

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

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