The general solution of differential equation d y d x = cos ( x + y ) is

Question

The general solution of differential equation d y d x = cos ( x + y ) is, tan ⁡ x + y 2 = y + c, tan ⁡ x + y 2 = x + c, cot ⁡ x + y 2 = y + c, cot ⁡ x + y 2 = x + c

MARKS App · Accepted Answer

Let x + y = v 1 + d y d x = d v d x d y d x = d v d x − 1 ∴ d v d x − 1 = cos v ⇒ d v d x = 1 + cos v ⇒ d v d x = 2 cos 2 v 2 ⇒ ∫ d v cos 2 v 2 = 2 ∫ d x ⇒ ∫ sec 2 ( v 2 ) d v = 2 x + c ⇒ 2 tan ( v 2 ) = 2 x + c ⇒ 2 tan ( x + y 2 ) = 2 x + c ⇒ tan ( x + y 2 ) = x + c 2 ⇒ tan ( x + y 2 ) = x + c

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