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Question
Solve the following differential equation:
`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`
Solution
The equation can be written as
`tan y ("d"y)/("d"x)` = cos(x + y) + cos(x – y)
W.K.T cos(A + B) + cos(A – B) = 2 cos A cos B
Here A = x, B = y
∴ `tan y ("d"y)/("d"x)` = 2 cos x cos y
`tany/cosy` dy = 2 cos x dx
Taking integration on both sides, we get
`int tany/cosy "d"y = 2int cos x "d"x`
`2 int tan y sec y "d"y = 2 int c x "d"x`
sec y = 2 sin x + C
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