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 &#60; 1 . If y 1 2 = 3 2 , then y - 1 2 is equal to

Aicharya · Accepted Answer

d y 1 - y 2 + d x 1 - x 2 = 0 &#8658; sin - 1 y + sin - 1 x = c At, x = 1 2 , &#8201; y = 3 2 &#8658; &#8201; c = &#960; 2 &#8658; &#8201; 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

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…

Solution

Let y = y x be a solution of the differential equation, 1 - x 2 d y d x + 1 - y 2 = 0 , x &#60; 1 . If y 1 2…

Solution

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…