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Vector Algebra

Question
CBSEENMA12033050

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            sec squared straight y space tanx space dy space equals space sec squared straight x space tan space straight y space dx
Separating the variables, we get,
                               fraction numerator sec squared over denominator tan space straight y end fraction dy space equals space minus fraction numerator sec squared straight x over denominator tan space straight x end fraction dx
Integrating,   log space open vertical bar tan space straight y close vertical bar space equals space minus log space open vertical bar tan space straight x close vertical bar space plus space log space straight A
or   log space open vertical bar tan space straight y close vertical bar space plus space log space open vertical bar tan space straight x close vertical bar space equals space log space straight A space or space log space open vertical bar tan space straight x space tany close vertical bar space equals space log space straight A
or   open vertical bar tan space straight x space tan space straight y close vertical bar space equals space straight A space space space space space space rightwards double arrow space space space tan space straight x space tan space straight y space equals space plus-or-minus straight A space space space or space space space tanx space tany space equals space straight c
where c is an arbitrary constant. 

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