Question

The general solution of the differential equation `y  "d"x - (1 + x^2) cot^-1 x  "d"y` = 0 is ______.

पर्याय

• `y cot^-1x = "c"`

• `x cot^-1y = "c"`

• `y + cot^-1x = "c"`

• `x + cot^-1y = "c"`

Answer 1

The general solution of the differential equation `y  "d"x - (1 + x^2) cot^-1 x  "d"y` = 0 is `y cot^-1x = "c"`.

Explanation:

`y  "d"x - (1 + x^2) cot^-1 x  "d"y` = 0

Integrating on both sides, we get

`int (-"d"x)/((1 + x^2)cot^-1x) + int ("d"y)/y = log "c"`

⇒ `log (cot^-1x) + log y = log "c"`

⇒ `log (y cot^-1x) = log "c"`

⇒ `y cot^-1x` = c