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  4. The integrating factor of (xdy/dx)-y=x4-3x is

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Q. The integrating factor of $ \frac{xdy}{dx}-y=x^{4}-3x$ is

VITEEEVITEEE 2019

Solution:

Since $x \frac{dy}{dx}-y=x^{4}-3x$
$\therefore \frac{dy}{dx}-\frac{y}{x}=x^{3}-3$
Hence
$IF=e^{\int\,P\,dx}=e^{-\int \frac{1}{x}dx}=e^{-log\,x}=\frac{1}{x}$