The solution of cos x frac{dy}{dx} + y sin x | vedclass

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Question

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

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$y \sec x = 	an x + c$

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(B) Given the differential equation: $\cos x \frac{dy}{dx} + y \sin x = 1$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: $I.F. = e^{\int P dx} = e^{\int 	an x dx} = e^{\ln |\sec x|} = \sec x$.The general solution is given by: $y 	imes (I.F.) = \int (Q 	imes I.F.) dx + c$Substituting the values: $y \sec x = \int (\sec x 	imes \sec x) dx + c$$y \sec x = \int \sec^2 x dx + c$$y \sec x = 	an x + c$.

The solution of $\cos x \frac{dy}{dx} + y \sin x = 1$ is

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