Solving a PDE: Simplifying Third Order Equation to Second Order Airy Equation

[ssatonreb]

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:

<br /> \frac{\partial^{3}F(x,y)}{\partial y^{3}}-ix(y+C)\frac{\partial F(x,y)}{\partial y}=0<br />

where C is positive constant i=\sqrt{-1}

Thank You.

 

[g_edgar]

F(x,y) itself does not appear in the equation. So for example define G(x,y) = \partial F(x,y)/\partial y to get a second-order equation for G . Also, there are no derivatives \partial/\partial x, so we might as well consider it an ordinary differential equation.

 

[ssatonreb]

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?