Let a solution y = y(x) of the differential equation x x^2 - 1 ,dy - y y^2 - 1 ,dx = 0 satisfy y(2) = 2 3 . STATEMENT-1 : y(x) = ( ^ -1 x - 6 ) and STATEMENT-2 : y(x) is given by 1 y = 2 3 x - 1 - 1 x^2

JEE Advanced 2008 Mathematics question

Let a solution y = y(x) of the differential equation

x dy - y dx = 0

satisfy . STATEMENT-1 : and STATEMENT-2 : y(x) is given by

= -

(A)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
(B)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
(C)STATEMENT-1 is True, STATEMENT-2 is FalseCorrect
(D)STATEMENT-1 is False, STATEMENT-2 is True

Answer: (C)

Separating variables: . At x = 2: and , so and \sec\sec^{-1}$x

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Question ID VK-037617