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Homework Help: Help with integrals needed

  1. Sep 6, 2008 #1
    (urgent) help with integrals needed

    I was doing an exercise on quasilinear equations, and have come to the point here I have to solve the following:

    [tex]dy=\frac{du}{x-u}[/tex], where [tex]u=u(x, y)[/tex].

    How do I integrate this?

    Thank you!
     
    Last edited: Sep 6, 2008
  2. jcsd
  3. Sep 6, 2008 #2

    HallsofIvy

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    Re: (urgent) help with integrals needed

    Saying that u is a function of x and y means that x depends upon u. The integral should depend strongly on just what that dependence is. How did you get that?
     
  4. Sep 6, 2008 #3
    Re: (urgent) help with integrals needed

    I'll write everything from the begining then, I probably got something wrong.

    I have to solve the following quasilinear equation:

    [tex]x u_x + y u_y= xy-yu[/tex]

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

    [tex]\frac{dx}{x}=\frac{dy}{y}=\frac{du}{y(x-u)}[/tex]


    [tex]\frac{dx}{x}=\frac{dy}{y}[/tex] gives me
    [tex]ln x=ln y + ln \overline{c}[/tex], [tex]\phi (x, y)=c=\frac{x}{y}[/tex]

    And now I try to do the same with [tex]\frac{dy}{y}=\frac{du}{y(x-u)}[/tex] to get [tex]\psi(x, y, u)[/tex], but don't know how.

    Please, help me.
     
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