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

Question

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

MARKS App · Accepted Answer

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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