Help with integrals needed

  • Thread starter iris_m
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  • #1
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(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!
 
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  • #2
HallsofIvy
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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?
 
  • #3
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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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