Question
For the following differential equation, find the general solution:
sec2 x tan y dx + sec2 y tan x dy = 0.
Solution
The given differential equation is
sec2 x tan y dx + sec2 y tan x dy = 0
or
Separating the variables, we get,

Integrating,
or
or
where c is an arbitrary constant.
sec2 x tan y dx + sec2 y tan x dy = 0
or

Separating the variables, we get,

Integrating,

or

or

where c is an arbitrary constant.