Let a curve y=y(x) be given by the solution of the differential equation \cos (\frac{1}{2} \cos ^{-1}({e}^{-{x}})) {dx} =\\sqrt{{e}^{2 {x}}-1} {dy} If it intersects y-axis at {y}=-1, and the intersection point of the curve with x-axis is (\\alpha, 0), then {e}^{\\alpha} is equal to ________. [20 Jul 2021 Shift 2]

Differential Equations Part 1

Section: Mathematics

Question : 20 of 100

Marks: +1, -0

Let a curve y=y(x) be given by the solution of the differential equation
cos(

cos−1(e−x))‌dx =√e2x−1dy
If it intersects y-axis at y=−1, and the intersection point of the curve with x-axis is (α,0), then eα is equal to ________.

[20 Jul 2021 Shift 2]

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