Help needed with Airy equation

  • Thread starter ssatonreb
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  • #1
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
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[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.
 
  • #3
5
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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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