The solution of frac{dy}{dx} + 2y tan x = sin | vedclass

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(B) The given equation is $\frac{dy}{dx} + 2y 	an x = \sin x$,which is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P =

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$y \sec^2 x = \sec x + c$

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(B) The given equation is $\frac{dy}{dx} + 2y 	an x = \sin x$,which is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P = 2 	an x$ and $Q = \sin x$.First,we find the Integrating Factor $(I.F.)$:$I.F. = e^{\int P dx} = e^{\int 2 	an x dx} = e^{2 \ln |\sec x|} = e^{\ln |\sec^2 x|} = \sec^2 x$.The general solution is given by $y \cdot (I.F.) = \int Q \cdot (I.F.) dx + c$.Substituting the values:$y \sec^2 x = \int \sin x \cdot \sec^2 x dx + c$.Since $\sin x \cdot \sec^2 x = \sin x \cdot \frac{1}{\cos^2 x} = 	an x \sec x$,we have:$y \sec^2 x = \int 	an x \sec x dx + c$.Integrating $\int 	an x \sec x dx$,we get $\sec x$.Thus,the solution is $y \sec^2 x = \sec x + c$.

The solution of $\frac{dy}{dx} + 2y \tan x = \sin x$ is

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