If y x is a solution of d y d x - x y 1 + x = 1 1 + x and y 0 = - 1 , then the value of y 2 is

Question

If y x is a solution of d y d x - x y 1 + x = 1 1 + x and y 0 = - 1 , then the value of y 2 is, - 1 2, - 1 3, - 1 4, - 1 5

MARKS App · Accepted Answer

I.F. = e - ∫ x 1 + x d x = e - ∫ x + 1 - 1 x + 1 d x = e - x + ln ⁡ x + 1 = e - x · | ( x + 1 ) | y · x + 1 e – x = ∫ x + 1 x + 1 e - x d x + c y · | ( x + 1 ) | e – x = - | x + 1 | x + 1 e - x + c ⇒ y = - 1 x + 1 + c e x | x + 1 | x = 0 , y = - 1 ⇒ - 1 = - 1 + c ⇒ c = 0 ⇒ y = - 1 1 + x y 2 = - 1 3

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