General solution of the differential equation | vedclass

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(A) The given differential equation is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P = 	an x$ and $Q = \sec x$. First,

Vedclass · Accepted Answer

$y \sec x = 	an x + c$

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

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

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