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PDE i.v.p. using method of characteristics

  1. Jun 26, 2012 #1
    1. The problem statement, all variables and given/known data
    solve x2ux + y2uy = 0 for u(2,y) = y

    2. Relevant equations
    3. The attempt at a solution

    with a = x2 and b = y2

    y' = b/a = (y/x)2 this can be solved for y by separation of variables:

    [itex]y = \frac{x}{1-xC}[/itex]
    and
    [itex]C = \frac{y-x}{xy}[/itex]

    now

    [itex]u(x,y) = f(C) = f(\frac{y-x}{xy})[/itex]

    applying initial value conditions

    [itex]u(2,y) = f(\frac{y-2}{2y})[/itex]

    this is where my understanding runs out. how do i determine f according to the initial value? i have looked at several books but they just assume this step is obvious
     
    Last edited: Jun 26, 2012
  2. jcsd
  3. Jun 26, 2012 #2
    have solved it now :smile: by taking a different approach and by converting to a system of ODEs and doing a coordinate transform from x(t) -> x(t,s) but I would still like to know how to solve it according to my original question, thanks
     
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