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  4. The integrating factor of the differential equation x (dy/dx) - y = 2x2

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Q. The integrating factor of the differential equation $x \frac{dy}{dx} - y = 2x^2$

Differential Equations

Solution:

$x \frac{dy}{dx} - y = 2x^{2} or \frac{dy}{dx} - \frac{y}{x} = 2x$
$ I.F. = e^{\int\frac{-1}{x}dx} = e^{-\log x} = e^{- \log x} =e^{\log \frac{1}{x}} = \frac{1}{x} $