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Question
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
Solution
sec2y tan x dy + sec2x tan y dx = 0
Dividing both sides by tan x tan y, we get
`(sec^2y tan x)/(tanx tan y) "d"y + (sec^2x tany)/(tanx tany) "d"x` = 0
∴ `(sec^2x)/(tanx) "d"x + (sec^2y)/(tany) "d"y` = 0
Integrating on both sides, we get
`int (sec^2x)/(tanx) "d"x + int (sec^2y)/(tany) "d"y` = 0
∴ log |tan x| + log |tan y| = log |c|
∴ log |tan x.tan y| = log |c|
∴ tan x tan y = c
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