Question

Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.

Options

• cosx

• tanx

• secx

• sinx

Answer 1

Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is secx.

Explanation:

The given differential equation is

`cos x * ("d"y)/("d"x) + y sinx` = 1

⇒ `("d"y)/("d"x) + sinx/cosx y = 1/cosx`

⇒ `("d"y)/("d"x) + tan x  y = secx`

Here, P = tan x and Q = sec x

∴ Integrating factor = `"e"^(int Pdx)`

= `"e"^(int tan x "d"x)`

= `"e"^(log secx)`

= sec x.