𝑑𝑦/𝑑𝑥 = 2 𝑐𝑜𝑠*2𝑦

Answer 1

dy/dx = 2 cos2y
dy/cos(2y) = 2 dx
now recall that ∫secy dy = ln|secy + tany|
and you get
1/2 ln|secy + tany| = 2x + C
secy + tany = ce^(4x)
That can be manipulated in several ways, none of them pretty