If x = x y is the solution of the differential equation y d x d y = 2 x + y 3 y + 1 e y , x 1 = 0 ; then x e is equal to

Question

If x = x y is the solution of the differential equation y d x d y = 2 x + y 3 y + 1 e y , x 1 = 0 ; then x e is equal to, e e e 3 - 1, e 3 e e - 1, e e - 1, e e e 2 - 1

MARKS App · Accepted Answer

Given d x d y - 2 x y = y 2 y + 1 e y Finding integrating factor I . F . = e ∫ − 2 y d x = e − 2 ln y = 1 y 2 ⇒ x y 2 = ∫ y + 1 e y d y ⇒ x y 2 = y · e y + C 0 = e + C ⇒ C = - e ⇒ x y 2 = y e y - e Putting y = e in the equation we get ⇒ x e 2 = e . e e - e ⇒ x = e 3 e e - 1

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