Question

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

Answer 1

Given differential equation is, $\frac{dy}{dx}-y\tan x=\cos x$

Comparing above differential equation with first order linear differential equation,

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

We get $P=-\tan x$ and $Q=\cos x$

So integrating factor is $e^{\int Pdx}=e^{\int -\tan xdx}=e^{-\ln \sec x}=e^{\ln \cos x}=\cos x$

Remember: $a^{{\log }_{a}x}=x$