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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The equation of the curve satisfying the differential equation x e x sin ⁡ y d y - x + 1 e x cos ⁡ y d x = y d y and passing through the origin is

Options

  1. Ax e x = y 2 cos y
  2. B2 x e x = y cos ⁡ y
  3. C2 x e x cos ⁡ y + y 2 = 0
  4. D2 x e x cos ⁡ y = y 2

Correct answer

C. 2 x e x cos ⁡ y + y 2 = 0

Step-by-step solution

The given equation is d - x e x cos ⁡ y = y d y On integrating, we get – x e x cos ⁡ y = y 2 2 + c As it passes through the origin, c = 0 ∴ the equation of the curve is 2 x e x cos ⁡ y + y 2 = 0

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