Let y = y x be a solution of the differential equation, 1 - x 2 d y d x + 1 - y 2 = 0 , x 1 . If y 1 2 = 3 2 , then y - 1 2 is equal to

Question

Let y = y x be a solution of the differential equation, 1 - x 2 d y d x + 1 - y 2 = 0 , x 1 . If y 1 2 = 3 2 , then y - 1 2 is equal to, 3 2, - 1 2, 1 2, - 3 2

MARKS App · Accepted Answer

d y 1 - y 2 + d x 1 - x 2 = 0 ⇒ sin - 1 y + sin - 1 x = c At, x = 1 2 , y = 3 2 ⇒ c = π 2 ⇒ s i n - 1 y = c o s - 1 x Hence, y - 1 2 = s i n c o s - 1 - 1 2 = 1 2

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