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## Homework Statement

I have 3 equations:

[itex]\frac{\partial^2 u}{\partial t^2}+\frac{\partial^2 u}{\partial x \partial t}+\frac{\partial^2 u}{\partial x^2}[/itex]

[itex]\frac{\partial^2 u}{\partial t^2}+4\frac{\partial^2 u}{\partial x \partial t}+4\frac{\partial^2 u}{\partial x^2}[/itex]

[itex]\frac{\partial^2 u}{\partial t^2}-4\frac{\partial^2 u}{\partial x \partial t}+\frac{\partial^2 u}{\partial x^2}[/itex]

I know their classification (first one is elliptical, second one is parabolic, third one is hyperbolic).

I need to find their characteristics. How do I do that?

What is a characteristic?

I think that the one who is elliptical has no characteristic, the parabolic has only one and the hyperbolic has two.