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JEE Main20208 Jan 2020Morning ShiftMathematicsDifferential EquationsActual

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

Options

  1. A3 2
  2. B- 1 2
  3. C1 2
  4. D- 3 2

Correct answer

C. 1 2

Step-by-step solution

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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