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Question
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
Options
`sinx/siny` = c
sinx siny = c
sinx + siny = c
cosx cosy = c
Solution
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is sinx siny = c.
Explanation:
The given differential equation is cosx siny dx + sinx cosy dy = 0
⇒ sinx cosy dy = – cosx siny dx
⇒ `cosy/siny "d"y = - cosx/sinx "d"x`
⇒ coty dy = – cotx dx
Integrating both sides, we have
⇒ `int coty "d"y = - int cot x "d"x`
⇒ `log|sin y| = - log|sin| + log"c"`
⇒ `log|siny| + log|sinx| = log"c"`
⇒ `log|siny . sin x| = log"c"`
⇒ sinx siny = c
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