The solution of the differential equation dydx−ytanx=exsecx is

dydx+−tanxy=exsecxp(x)=−tanx,Q(x)=exsecxI.F=e∫pdx=cosxycosx=∫exsecxcosxdxycosx=ex+c

The solution of the differential equation dydx−ytanx=exsecx is

dydx+−tanxy=exsecxp(x)=−tanx,Q(x)=exsecxI.F=e∫pdx=cosxycosx=∫exsecxcosxdxycosx=ex+c

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The solution of the differential equation $\frac{d y}{d x} - y \tan x = e^{x} \sec x$ is

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y = e^xcosx + c

y cosx = e^x + c

y = e^xsinx + c

y sinx = e^x + c

answer is B.

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Detailed Solution

$\frac{d y}{d x} + (- \tan x) y = e^{x} \sec x$

$p (x) = - \tan x, Q (x) = e^{x} \sec x$

$I . F = e^{\int p d x} = \cos x$

$y \cos x = \int e^{x} \sec x \cos x d x$

$y \cos x = e^{x} + c$

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The solution of the differential equation dydx−ytanx=exsecx is

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The solution of the differential equation $\frac{d y}{d x} - y \tan x = e^{x} \sec x$ is