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Math Help - help with integrals needed

  1. #1
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    help with integrals needed

    I have to solve the following:

    <br />
dy=\frac{du}{x-u}, where u=u(x, y).

    How do I solve this?
    Thank you so much for all your help!
    Last edited by georgel; September 6th 2008 at 11:08 AM.
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  2. #2
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    Quote Originally Posted by georgel View Post
    I have to solve the following:

    <br />
dy=\frac{du}{x-u}, where u=u(x, y).

    How do I solve this?
    Thank you so much for all your help!
    Is this exactly as the original question is stated?
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Is this exactly as the original question is stated?
    No. I have to solve a quasilinear equation:

    x u_x + y u_y= xy-yu

    I'm trying to find the general soultion so I do the standard procedure from my textbook:

    \frac{dx}{x}=\frac{dy}{y}=\frac{du}{y(x-u)}


    \frac{dx}{x}=\frac{dy}{y} gives me
    ln x=ln y + ln c, \phi (x, y)=c=\frac{x}{y}

    And now I try to do the same with \frac{dy}{y}=\frac{du}{y(x-u)} to get \psi(x, y, u), but don't know how.
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  4. #4
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    I've had a similar problem:

    \frac{dy}{y+u}=\frac{du}{y-u}, and this is what I did:

    ydy-udy=ydu+udu
    (y-u)dy-(y-u)du=2udu
    Then I substituted z=y-u and got zdz=2udu.

    But I don't know what to do with the problem I stated above..
    Please, could anyone help?

    I'm stuck and unfortunately, I'm running out of time to solve it.
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