Let a curve y = y(x) be given by the solution of the differential equation cos (1/2 cos ⁻¹(e⁻ˣ))dx = √(e²ˣ - 1) dy. 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 _ _ _ _ _ _ _ _ _.

Differential Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 20 Jul, Evening shift · Q34

JEE Main 202120 Jul, Evening shiftMathematicsMediumDifferential Equations163× since 2002

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

\cos \left( {{1 \over 2}{{\cos }^{ - 1}}({e^{ - x}})} \right)dx = \sqrt {{e^{2x}} - 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 __________________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Differential Equations Question with Answer (20 Jul Evening shift, Q34) | JEE Arc