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Let y x is the solution of the differential equation x + 2 d y d x - x + 1 y = 2 . If y 0 = - 1 , then the value of y 2 is equal to

Options

  1. Ae 2 + 1 2
  2. Be 2 - 1 2
  3. C1 2 - e 2
  4. De 2

Correct answer

B. e 2 - 1 2

Step-by-step solution

Given differential equation is d y d x - x + 1 x + 2 y = 2 x + 2 I.F. = e - ∫ x + 1 x + 2 d x = e - x x + 2 So the solution of the equation is y x + 2 e - x = - 2 e - x + C Since y 0 = 1 , we have C = 4 So y 2 = e 2 - 1 2

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