Question

The solution of differential equation coty dx = xdy is ______.

Answer 1

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