The integrating factor of $sin x\frac{dy}{dx}+2ycos x=4$ is :

|sin x| $|sin x|^2$ $|sin x^2|$ $|cos x|$

$|sin x|^2$

The correct answer is Option (2) → $|\sin x|^2$ $\sin x\frac{dy}{dx}+2y\cos x=4$ $\frac{dy}{dx}+2y\frac{\cos x}{\sin x}=\frac{4}{\sin x}$ dividing by $\sin x$ $I.F.=e^{\int\frac{2\cos x}{\sin x}}dx=e^{2\log|\sin x|}=|\sin x|^2$