The solution of the differential equation x d x + y sin 2 ⁡ x d y = y d y + x sin 2 ⁡ y d x is (where, c is an arbitrary constant)

Question

The solution of the differential equation x d x + y sin 2 ⁡ x d y = y d y + x sin 2 ⁡ y d x is (where, c is an arbitrary constant), x tan ⁡ x = sec ⁡ y + c, x tan ⁡ y = sec ⁡ x + c, x tan ⁡ x - ln ⁡ sec ⁡ x = y tan ⁡ y - ln ⁡ sec ⁡ y + c, x tan ⁡ x = ln ⁡ sec ⁡ y + c

MARKS App · Accepted Answer

The given equation is x cos 2 ⁡ y d x = y cos 2 ⁡ x d y ∫ x sec 2 ⁡ x d x = ∫ y sec 2 ⁡ y d y Using integration by parts, we get, x tan ⁡ x - ln ⁡ sec ⁡ x = y tan ⁡ y - ln ⁡ sec ⁡ y + c

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