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The differential equation obtained by eliminating the arbitrary constants a and b from x y = a e x + b e - x is

Options

  1. Ax d 2 y d x 2 + 2 d y d x - x y = 0
  2. Bd 2 y d x 2 + 2 y d y d x - x y = 0
  3. Cx d 2 y d x 2 + 2 d y d x + x y = 0
  4. Dd 2 y d x 2 + d y d x - x y = 0

Correct answer

A. x d 2 y d x 2 + 2 d y d x - x y = 0

Step-by-step solution

Given, x y = a e x + b e - x ..... (I) ⇒    x   d y d x + y = a e x - b e - x ⇒    x   d 2 y d x 2 + d y d x + d y d x = a e x + b e - x ⇒    x   d 2 y d x 2 + 2   d y d x - x y = 0 [from eq. (I)]

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