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  4. Integrating factor of the differential equation cosx (dy/dx)+y sin x=1 is

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Q. Integrating factor of the differential equation
$cosx \frac{dy}{dx}+y\,sin\,x=1$ is

Differential Equations

Solution:

$cosx \frac{dy}{dx}+ysin\,x=1$
$\Rightarrow \frac{dy}{dx}+\frac{sin\,x}{cos\,x}\cdot y=\frac{1}{cos\,x}$
$\Rightarrow \frac{dy}{dx}+tan\,x\cdot y=sec\,x$
$I.F.=e^{\int tan\,xdx}=e^{log\left(sec\,x\right)}=sec\,x$