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Homework Help: Finding general solution to this pde

  1. Jun 10, 2012 #1
    Hi, my equation is;

    \frac{\partial}{\partial t}U(x,y,t) = 2g \left( x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) U(x,y,t)

    I want to find the general solution to this but I don't know how to find it?

    Any help would be great...thanks :D
  2. jcsd
  3. Jun 10, 2012 #2
    What class is this for, a PDE class???

    What have you tried already?
  4. Jun 11, 2012 #3
    Yer its PDE class.

    I've tried using Charactoristics, so,

    \frac{\partial x(t)}{\partial s} = 2gy(t)


    \frac{\partial y(t)}{\partial s} = -2gx(t)

    With s=t. I am not sure what to do now with regards to forming a general solution, would it be something of the form,

    U(x,y,t) = f (x_0 +2gy(t)t, y_0 -2gx(t)t, t)

    I'm not sure how to proceed.

  5. Jun 11, 2012 #4


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    Writing the original equation in polar coordinates should be illuminating. There's a further linear change of variables that will put the equation into a form where the general solution should be obvious.
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