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The solution of the differential equation x d y + y x d x = d x x is (where, c is an arbitrary constant)

Options

  1. Ay = 1 + c e 1 / x
  2. By = c e 1 / x
  3. Cy = c e 1 / x - 1
  4. Dx y = 1 - c e 1 / x

Correct answer

A. y = 1 + c e 1 / x

Step-by-step solution

The given differential equation can be written as, d y d x + 1 x 2 ⋅ y = 1 x 2 Integrating factor is e - 1 / x ⇒ y . e - 1 / x = ∫ 1 x 2 . e - 1 / x   d x Hence, the solution is y = 1 + c e 1 / x

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