The integrating factor of frac{dy}{dx} + frac | vedclass

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Question

(A) The given differential equation is of the form $\frac{dy}{dx} + Py = Q$,where $P = \frac{1}{x}$ and $Q = x^3 - 3$.The integrating factor $(I.F.)$

Vedclass · Accepted Answer

$x$

Vedclass · Answer

(A) The given differential equation is 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 the value of $P$,we get $I.F. = e^{\int \frac{1}{x} dx}$.Since $\int \frac{1}{x} dx = \log_e x$,we have $I.F. = e^{\log_e x}$.Using the property $e^{\log_e x} = x$,the integrating factor is $x$.

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

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