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The solution of the differential equation d y d x = x y + y x y + x is y - λ x = ln ⁡ x y + C (where, C is an arbitrary constant and x , y > 0 ). Then, the value of λ is equal to

Options

  1. A1
  2. B1 2
  3. C2
  4. D4

Correct answer

A. 1

Step-by-step solution

The given equation is 1 + 1 y d y = 1 + 1 x d x On integrating, we get, y + ln ⁡ y = x + ln ⁡ x + C or y - x = ln ⁡ x y + C ∴ λ = 1 .

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