Question

The integrating factor of the differential equation $\frac{dy}{dx}-y\tan x=\cos x$ is,

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

Answer 1

Answer: (A)

$\cos x$

We have,

$\frac{dy}{dx}-y\tan x=\cos x$

We know that the general equation

$\frac{dy}{dx}+Py=Q$

So,

$P=-tanx,Q=\cos x$

We know that

$I.F=e^{\int Pdx}$

Therefore,

$I.F=e^{\int \tan xdx}$

$I.F=e^{-\ln |\cos x|}$

$I.F=e^{\ln \left(\frac{1}{\sec x}\right)}$

$I.F=\frac{1}{\sec x}$

$I.F=\cos x$

Hence, this is the answer.