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Help needed with Airy equation

  1. Jul 9, 2009 #1
    Hello!

    I have difficulty to solve a PDE. I'm trying to simplify the third order eq. into the second order Airy equation. But I can't see where I could start. Could you, please, help me.
    Where should I start?
    Equations is:

    [tex]
    \frac{\partial^{3}F(x,y)}{\partial y^{3}}-ix(y+C)\frac{\partial F(x,y)}{\partial y}=0
    [/tex]

    where C is positive constant [tex] i=\sqrt{-1} [/tex]

    Thank You.
     
  2. jcsd
  3. Jul 9, 2009 #2
    [tex]F(x,y)[/tex] itself does not appear in the equation. So for example define [tex]G(x,y) = \partial F(x,y)/\partial y[/tex] to get a second-order equation for [tex]G[/tex] . Also, there are no derivatives [tex]\partial/\partial x[/tex], so we might as well consider it an ordinary differential equation.
     
  4. Jul 9, 2009 #3
    Thank You, but Airy equations is witten as f(y)''-y*f(y)=0.

    How can I simplify eq. in order to -ix(y+C) become y?
     
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