Solve the differential equation `(1 + cos 2x) + (1- cos 2y) (dx)/(dy) = 0`

Explanation

`(1+cos 2x) dy + (1- cos 2y) dx = 0`
`rArr (dy)/(1-cos 2y) + (dx)/(1+cos 2x) = 0`
Integrating both sides
`rArr (1)/(2)int (1)/(sin^(2)y) dx + (1)/(2) int (1)/(cos^(2)x)dx = C_(1)`
`rArr int cosec^(2) y dy + int sec^(2) x dx = C_(1)`
`rArr -cot y + tan x = C`
`rArr tan x - cot y = C`
which is the general solution of the given differential equation.