(sec x)^(y)=(tan y)^(x)

If (cos x)^(y)=(tan y)^(x), prove that (dy)/(dx)=(log tan y+y tan x)/(log cos x-x sec y cos ecy)

(dy)/(dx)+(y)/(2)sec x=(tan x)/(2y)

Solution of the differential equation cos xdy=y(sin x-y)dx,0

If tan x+tan y=(sec x+sec y)/(cos x+cos y).(dy)/(dx) then which of the following is correct (1) sec(x+y)-tan(x+y)=x+c (2) sec(x+y)+tan(x+y)=x+c (3) tan(x+y)-sec(x+y)=x+c (4) None of these

((ln (sec x + tan x)) / (cos x) dx = ((ln (sec y + tan y)) / (cos y) dy

lim_(x rarr0)((x+y)sec(x+y)-x sec x)/(y) is equal to sec x(x tan x+1)(b)x tan x+sec xx sec x+tan x(d) none of these

[x tan ((y) / (x)) - y sec ^ (2) ((y) / (x))] dx + x sec ^ (2) ((y) / (x))] dy = 0

2 (dy) / (dx) -y sec x = y ^ (3) tan x

sec ^ (2) y (dy) / (dx) + x tan y = x ^ (3)