Question

Integrating Factor of the differential equation $\frac{dy}{dx}=\tan x+e^x$ ______.

• A. $\sin x$
• B. $\sec x$
• C. $\cos x$
• D. $\cot x$

Answer 1

Answer: (C)

$\cos x$

$\frac{dy}{dx}=y\tan x+e^x$
$\therefore \frac{dy}{dx}-y\tan x=e^x$
Which is linear differential equation of the type.
$\frac{dy}{dx}+yP\left(x\right)=Q\left(x\right)$
We have $P\left(x\right)=-\tan x$
Integrating Factor $(I.F)=e^{\int P\left(x\right)dx}=e^{\int -\tan xdx}=e^{-\log \left(\sec x\right)}=e^{\log \left(\cos x\right)}=\cos x$