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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The solution of the differential equation cos ⁡ x d y d x + y sin ⁡ x = 1 is (where, c is an arbitrary constant)

Options

  1. Ay = c sin ⁡ x + cos ⁡ x
  2. By = sin ⁡ x + c cos ⁡ x
  3. Cy = tan ⁡ x + c
  4. Dy sin ⁡ x = sin ⁡ x + c

Correct answer

B. y = sin ⁡ x + c cos ⁡ x

Step-by-step solution

d y d x + y tan ⁡ x = sec ⁡ x Ι . F . = e ∫ tan ⁡ x d x = e l o g s e c x = sec ⁡ x Hence, the solution is, y ⋅ sec ⁡ x = ∫ s e c 2 x d x ⇒ y sec ⁡ x = tan ⁡ x + c ⇒ y = sin ⁡ x + c cos ⁡ x

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