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Let a curve y = y (x) be given by the so...

Let a curve y = y (x) be given by the solution of differential equation `cos ((1)/(2) cos ^(-1) (e ^(-x)) ) dx = sqrt ( e ^( 2x) - 1)dy` If it intersects y – axis at y = –1, and the intersection point point of the curve with x – axis is `(alpha, theta),` then `e ^(alpha)` is equal to __________.

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