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The differential equation sec²x·tan y dx + sec²y·tan x dy = 0 has which general solution?
- tan y · tan x = c
- tan y / tan x = c
- tan²x / tan y = c
- None of these
Correct answer: tan y · tan x = c
Solution
Dividing by tan x*tan y gives (sec^2 x/tan x)dx + (sec^2 y/tan y)dy=0. Integrating: ln|tan x|+ln|tan y|=const, i.e. tan x*tan y = c.
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