Question

The solution of the differential equation `1 + "dy"/"dx" = (sin^2(x + y))/(cos (x + y))` is

पर्याय

• cosec (x + y) + tan(x + y) =x + c

• x + cosec (x + y) = c

• x + tan(x + y) = c

• x + sec(x + y) = c

Answer 1

x + cosec (x + y) = c

Explanation:

`1 + "dy"/"dx" = (sin^2(x + y))/(cos (x + y))`   ...(i)

Put x + y = v   ...(ii)

`1 + "dy"/"dx" = "dv"/"dx"`   ...(iii)

Substituting (ii) and (iii) in (i), we get

`=> "dv"/"dx" = (sin^2"v")/(cos "v")`

Integrating on both sides, we get

`int "dx" - int (cos v)/(sin^2"v")`dv = c

`=> x - (- 1/(sin v))` = c   ....[Put sin v = t ⇒ cos v dv = dt]

⇒ x + cosec v = c

⇒ x + cosec (x + y) = c