Let y = y(x) be the solution of the differential equation (1 - x^ 2 )dy = (xy + (x^ 3 + 2) 1 - x^ 2 )dx, −1 < x < 1, and y(0) = 0. If _ -1/2 ^ 1/2 1 - x^ 2 y(x)dx = k, then k^ -1 is equal to _____.

JEE Main 2022 Mathematics question

Let y = y(x) be the solution of the differential equation , −1 < x < 1, and y(0) = 0. If y(x)dx = k, then is equal to .

Answer: 320

dy/dx − xy/(1 − ). The integrating factor is , so , and y(0) = 0 gives c = 0. (The printed working uses ,

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Question ID VK-034533