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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The solution of the differential equation 2 y d x + x d y = 2 x y d x is (where, C is an arbitrary constant)

Options

  1. Ax y = x + C
  2. Bx y = x 2 2 + C
  3. Cx y = x + C
  4. Dx y = C

Correct answer

B. x y = x 2 2 + C

Step-by-step solution

Given equation can be written as d x y + x 1 2 y d y = x d x or d x y = x d x ∫ d x y = ∫ x d x ⇒ x y = x 2 2 + C

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