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sec^(2)x tany dx + sec^(2)y tan x dy = d...

` sec^(2)x tany dx + sec^(2)y tan x dy = dy =0`

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`sec^(2) tan y dx + sec^(2) y. tan x dy =0`
` (sec^(2)x)/(tanx) dx + (sec^(2)y)/(tan y) dy =0`
Integrating , we get ,
` int (sec^(2)y)/(tanx) dx + int(sec^(2)y)/(tany) dy = c_(1)`
Each of these integrals is of the type
`int(f'(x))/(f(x)) dx = log |f(x)|+c`
the general solution is
`log |tan x| + |log |tan y| = log c, " where " c_(1) = log c `
` log|tan x. tany | = log c`
tan x. tan y = c
This is the general solution.
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