The integrating factor of the differential eq | vedclass

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Question

(C) The given differential equation is $\frac{dy}{dx} + \frac{1}{x}y = x^3 - 3$. This is a linear differential equation of the form $\frac{dy}{dx} + P

Vedclass · Accepted Answer

$x$

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(C) The given differential equation is $\frac{dy}{dx} + \frac{1}{x}y = x^3 - 3$. This is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P = \frac{1}{x}$ and $Q = x^3 - 3$. The integrating factor ($I$.$F$.) is given by the formula $I.F. = e^{\int P dx}$. Substituting $P = \frac{1}{x}$,we get $I.F. = e^{\int \frac{1}{x} dx} = e^{\ln|x|} = x$. Therefore,the integrating factor is $x$.

The integrating factor of the differential equation $\frac{dy}{dx} + \frac{1}{x}y = x^3 - 3$ is

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