Question

Integrating factor of the differential equation
$cosx\frac{dy}{dx}+ysinx=1$ is

• A. $cosx$
• B. $tanx$
• C. $secx$
• D. $sinx$

Answer 1

Answer: (C)

$cosx\frac{dy}{dx}+ysinx=1$
$\Rightarrow \frac{dy}{dx}+\frac{sinx}{cosx}\cdot y=\frac{1}{cosx}$
$\Rightarrow \frac{dy}{dx}+tanx\cdot y=secx$
$I.F.=e^{\int tanxdx}=e^{log\left(secx\right)}=secx$