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If the solution of the differential equation y 3 x 2 cos ⁡ x 3 d x + sin ⁡ x 3 y 2 d y = x 3 d x is 2 sin ⁡ x 3 y k = x 2 + C ( where C is an arbitrary constant), then the value of k is equal to

Options

  1. A3
  2. B2
  3. C1
  4. D4

Correct answer

A. 3

Step-by-step solution

The given equation is y 3 ⋅ 3 x 2 cos ⁡ x 3 d x + sin ⁡ x 3 3 y 2 d y = x d x ⇒ d s i n x 3 ⋅ y 3 = x d x On integrating, we get, sin ⁡ x 3 ⋅ y 3 = x 2 2 + C ⇒ k = 3 .

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