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Let y = f x be the solution of the differential equation d y d x = - 2 x y - 1 with f 0 = 1 , then l i m x → ∞ f x is equal to

Options

  1. A1 2
  2. B0
  3. Ce
  4. D1

Correct answer

D. 1

Step-by-step solution

d y d x = - 2 x y - 1 d y d x + 2 x y = 2 x Ι . F . = e ∫ 2 x d x = e x 2 y ⋅ e x 2 = ∫ e x 2 2 x d x y ⋅ e x 2 = e x 2 + C ∵ y 0 = 1 ⇒ 1 = 1 + C ⇒ C = 0 Hence, the solution is y e x 2 = e x 2 ⇒ y = 1 = f x l i m x → ∞ f x = 1

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