1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]
    [itex]C = \frac{y-x}{xy}[/itex]


    [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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook