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PDE question

  1. Feb 6, 2009 #1
    Hi,

    This is a question in my calculus book that is frustrating me!

    By changing variables to [tex]u[/tex] and [tex]v[/tex], where [tex]u=\alpha(x)y[/tex] and [tex]v=y/x[/tex] with a suitable function [tex]\alpha(x)[/tex] to be determined, find the general solution of the equation [tex]x\frac{\partial f}{\partial x} - 2y\frac{\partial f}{\partial y}=6f(x,y)[/tex].

    I can see that the LHS of the equation looks similar to the chain rule, but I can't see how to continue...

    Thanks :)
     
  2. jcsd
  3. Feb 7, 2009 #2

    Hootenanny

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    HINT:

    Can you write [itex]\partial f/\partial x[/itex] and [itex]\partial f/\partial y[/itex] in terms of [partial] derivatives with respect to u, v, x and y?
     
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