The slope of the tangent to a curve C: y=y(x) at any point (x, y) on it is (2 e²ˣ-6 e⁻ˣ+9)/(2+9 e⁻²ˣ). If C passes through the points (0, 1/2+(π)/(2 √(2))) and (α, 1/2 e^(2 α)), then e^(α) is equal to:

(B) 3/(√(2))((3+√(2))/(3-√(2)))

(C) 1/(√(2))((√(2)+1)/(√(2)-1))

Differential Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Morning shift · Q3546

JEE Main 202225 Jul, Morning shiftMathematicsHardDifferential Equations163× since 2002

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 :