Question

Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.

Options

• cosx

• secx

• e^cosx

• e^secx

Answer 1

Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is secx.

Explanation:

Given differential equation is `("d"y)/("d"x) + y tanx - secx` = 0

⇒ `("d"y)/("d"x) + ytanx` = secx

Here, P = tanx and Q = secx

∴ I.F. = `"e"^(intPdx)`

= `"e"^(inttanx  "d"x)`

= `"e"^(log secx)`

= secx