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Thread: Ode

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

    Ode

    Find the Integrating Factor for the following :-

    $\displaystyle xdy - ydx = x^2dy$

    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:

    $\displaystyle
    y' + \frac{1}
    {{x^2 - x}}y = 0$

    so the integrating factor is:

    $\displaystyle
    \mu (x) = e^{\int {\frac{1}
    {{x(x - 1)}}dx} } = e^{\int {\frac{1}
    {{x - 1}} - \frac{1}
    {x}dx} } = \frac{{x - 1}}
    {x}
    $
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