The integrating factor of the differential eq | vedclass

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Question

(C) Given differential equation is $\cos x \frac{dy}{dx} + y \sin x = 1$. Dividing both sides by $\cos x$,we get: $\frac{dy}{dx} + y 	an x = \sec x$.

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$\sec x$

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(C) Given differential equation is $\cos x \frac{dy}{dx} + y \sin x = 1$. Dividing both sides by $\cos x$,we get: $\frac{dy}{dx} + y 	an x = \sec x$. This is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P = 	an x$ and $Q = \sec x$. The integrating factor $(I.F.)$ is given by $e^{\int P \, dx}$. $I.F. = e^{\int 	an x \, dx} = e^{\ln |\sec x|} = \sec x$. Thus,the correct option is $C$.

The integrating factor of the differential equation $\cos x \frac{dy}{dx} + y \sin x = 1$ is

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