How can I solve: dy/dx + (1 + cos2y) / (1 - cos2y) =0?

Answer 1

First thing to do is use the double angle identities where 1 + cos2y = 2cos²y and 1 - cos2y = 2sin²y. Now the differential equation becomes dy/dx + ctn²y =0 and dytan²y + dx =0 So using tan²y = sec²y -1 the equation becomes (sec²y -1) = -dx which when integrated gives tany -y = -x + C or y -tany = x+ C.