Question

The solution of the differential equation `dy/dx - cos^2y = 0` is ______ 

Options

• y + 2 cos y = c

• y - 2 sin y = c

• x = tan y + c

• y = tan x + c

Answer 1

The solution of the differential equation `dy/dx - cos^2y = 0` is x = tan y + c.

Explanation:

`dy/dx - cos^2y = 0`

 ⇒ `dy/dx = cos^2y`

 ⇒ `dy/dx = 1/(sec^2y)`

Integrating on both sides, we get

`int dx = intsec^2y dy + c`

 ⇒ x = tan y + c