Integrating factor of the differential equati | vedclass

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Question

(C) The given differential equation is $\frac{dy}{dx} + y 	an x = \sec x$.This is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$

Vedclass · Accepted Answer

$\frac{1}{\cos x}$

Vedclass · Answer

(C) The given differential equation is $\frac{dy}{dx} + y 	an x = \sec x$.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 the formula $I.F. = e^{\int P \, dx}$.Substituting $P = 	an x$,we get $I.F. = e^{\int 	an x \, dx}$.Since $\int 	an x \, dx = \ln|\sec x|$,we have $I.F. = e^{\ln(\sec x)}$.Using the property $e^{\ln(f(x))} = f(x)$,we get $I.F. = \sec x$.Since $\sec x = \frac{1}{\cos x}$,the correct option is $C$.

Integrating factor of the differential equation $\frac{dy}{dx} + y \tan x = \sec x$ is

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