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Question
The solution of differential equation coty dx = xdy is ______.
Solution
The solution of differential equation coty dx = xdy is x = C sec y.
Explanation:
The given differential equation is cot y dx = x dy
⇒ `("d"y)/(cot y) = ("d"x)/x`
⇒ tan y dy = `("d"x)/x`
Integrating both sides, we get
`int tan y "d"y = int ("d"x)/x`
⇒ `log sec y = log x + log "c"`
⇒ `log sec y - log x = log "c"`
⇒ `log|(sec y)/x| = log "C"`
∴ `secy/x` = C
⇒ `x/(sec y) = 1/"C"`
⇒ `x/secy` = C ....`[1/"c" = "C"]`
∴ x = C sec y
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