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Question
Solve the following differential equation:
cos x . cos y dy − sin x . sin y dx = 0
Solution
cos x . cos y dy − sin x . sin y dx = 0
`cos y/sin y dy - (sin x)/cos x dx = 0`
Integrating both sides, we get
∫ cot y dy − ∫ tan x dx = c1
∴ log |sin y| − [− log |cos x|] log c, where c1 = log c
∴ log |sin y| + log |cos x| = log c
∴ log |sin y . cos x| = log c
∴ sin y . cos x = c
This is the general solution.
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