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Math Help - Ode

  1. #1
    Member Altair's Avatar
    Joined
    Jan 2008
    Posts
    87

    Ode

    Find the Integrating Factor for the following :-

    xdy - ydx = x^2dy

    Please do tell the rule which is applied here.
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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    there is no special rule, just rewrite the equation:

    <br />
y' + \frac{1}<br />
{{x^2  - x}}y = 0

    so the integrating factor is:

    <br />
\mu (x) = e^{\int {\frac{1}<br />
{{x(x - 1)}}dx} }  = e^{\int {\frac{1}<br />
{{x - 1}} - \frac{1}<br />
{x}dx} }  = \frac{{x - 1}}<br />
{x}<br />
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