Let a curve y=y(x) be given by the solution of the differential equation cos(12cos−1(e−x))dx=√e2x−1dyIf 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:_____.

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

1.	Let a curve y=y(x) be given by the solution of the differential equation cos(12cos−1(e−x))dx=√e2x−1dyIf 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:_____.
Answer» Let a curve $y = y (x)$ be given by the solution of the differential equation $cos (\frac{1}{2} {cos}^{- 1} (e^{- x})) d x = \sqrt{e^{2 x} - 1} d y$ If it intersects $y -$ axis at $y = - 1,$ and the intersection point of the curve with $x -$ axis is $(α, 0),$ then $e^{α}$ is equal to:_____.