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The curve having differential equation, x cos ⁡ y d y d x + sin ⁡ y = x and passing through the origin, also passes through

Options

  1. A2 , π 2
  2. B- 2 , π 2
  3. C4 , 3 π 2
  4. D- 8 , 3 π 2

Correct answer

A. 2 , π 2

Step-by-step solution

Given equation is x cos ⁡ y d y + sin ⁡ y d x = x d x Or d x sin ⁡ y = x d x Integrating, we get ∫ d x sin ⁡ y = ∫ x d x ⇒ x sin ⁡ y = x 2 2 + C Since, it passes through 0 , 0 C = 0 ⇒ x sin ⁡ y = x 2 2

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