Question

The integrating factor of the differential equation dy/dx+ycotx=2cosx is
(A) sinx
(B) logsinx
(C) cotx
(D) coSX
is eyac If​

Answer 1

$\tt \frac{dy}{dx} + ycotx = 2 cosx \\ \\ \tt \boxed{\bold{\underline{\green{\tt Integrating\:factor= {e}^{\int P\:dx}}}}} \\ \\ \tt Here\:P = cotx \\ \\ \tt \therefore I.F = {e}^{\int cotx\:dx } \\ \\ \tt \therefore I.F = {e}^{{log}_{e}{sinx}} \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Integrating\:factor = sinx }}}}$