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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The solution of the differential equation d y d x = x - y x - 3 y is (where, c is an arbitrary constant)

Options

  1. A2 x y = x 2 + 3 y + c
  2. Bx y = x 2 + y 2 + c
  3. C2 x y = x 2 + 3 y 2 + c
  4. Dx y = x 2 + x

Correct answer

C. 2 x y = x 2 + 3 y 2 + c

Step-by-step solution

Given equation is x d y - 3 y d y = x d x - y d x ⇒ x d y + y d x = x d x + 3 y d y or d x y = x d x + 3 y d y On integrating, we get, x y = x 2 2 + 3 y 2 2 + k or 2 x y = x 2 + 3 y 2 + c

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