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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

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

Options

  1. Ax y = x + y + C
  2. Bx y = x 2 + y 2 2 + C
  3. Cln ⁡ x y = x 2 + y 2 + C
  4. D2 ln ⁡ x y = x 2 + y 2 + C

Correct answer

D. 2 ln ⁡ x y = x 2 + y 2 + C

Step-by-step solution

The given equation is 1 x y ⋅ y d x - x d y y 2 = x d x + y d y or d ln ⁡ x y = x d x + y d y On integrating, we get, ∫ d ln ⁡ x y = ∫ x d x + ∫ y d y ⇒ ln ⁡ x y = x 2 2 + y 2 2 + k ⇒ 2 ln ⁡ x y = x 2 + y 2 + C

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