Help needed with Airy equation

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:

$$\frac{\partial^{3}F(x,y)}{\partial y^{3}}-ix(y+C)\frac{\partial F(x,y)}{\partial y}=0$$

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

Thank You.

$$F(x,y)$$ 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.