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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The solution of the differential equation d y d x = x - y x + 4 y is (where C is the constant of integration)

Options

  1. Ax y + y 2 = x + C
  2. Bx y - y 2 = x 2 + C
  3. Cx y + 2 y 2 = x 2 + C
  4. D2 x y + 4 y 2 = x 2 + C

Correct answer

D. 2 x y + 4 y 2 = x 2 + C

Step-by-step solution

Given equation is x d y + 4 y d y = x d x - y d x or x d y + y d x + 4 y d y = x d x or d x y + 4 y d y = x d x Integrating, we get x y + 2 y 2 = x 2 2 + C

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