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  4. If the integrating factor of the differential equation (dy/dx)+p(x)t=Q(x) is x then P(x) is

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Q. If the integrating factor of the differential equation $ \frac{dy}{dx}+p(x)t=Q(x) \, is \, x$ then $ P(x) $ is

KEAMKEAM 2007Differential Equations

Solution:

Given that, $ IF=x $
$ \therefore $ $ {{e}^{\int{P}\,dx}}=x $
$ \Rightarrow $ $ \int{P}\,dx=\log x $
$ \Rightarrow $ $ P=\frac{d}{dx}\log x=\frac{1}{x} $