Question

The integrating factor of the differential equation cos2xdy/dx+y=tanx is
(A) sec2
(B) cos2x
(C) powerofe is tanx
(D) tan3​

Answer 1

$\tt {cos}^{2}x \frac{dy}{dx} + y = tanx \\ \\ \tt \therefore \frac{dy}{dx} + \frac{y}{{cos}^{2}x} = \frac{tan x}{{cos}^{2}x} \\ \\ \tt \therefore \frac{dy}{dx} + {sec}^{2}x.y = tanx.{sec}^{2}x \\ \\ \tt Here \: P = {sec}^{2}x \\ \\ \tt \therefore \boxed{\bold{\underline{\green{\tt Integrating\:factor= {e}^{\int P \:dx} }}}} \\ \\ \tt \therefore I.F = {e}^{\int {sec}^{2}x \:dx} \\ \\ \tt \therefore I.F = {e}^{tanx} \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Integrating\:factor = {e}^{tanx} }}}}$

Answer 2

$\huge\fbox \red{✔AN} {\colorbox{crimson}{SW}}\fbox\red{ER✔}$

(B) cos2x is the Correct Answer.

• I Hope it's Helpful My Friend.