Starting out in pde

Homework Statement

Hey I'm trying to get a sense of this problem, just starting pde class:

$$au_x+bu_y+cu=0$$

The Attempt at a Solution

Dunno what to do with that last term

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fzero
Homework Helper
Gold Member
Have you tried separation of variables?

hunt_mat
Homework Helper
This equation can be solved via the method of characteristics.

what is the method of characteristics?

hunt_mat
Homework Helper
This is something which should be covered in your course or alternatively you can google it ot it should be in any good book on PDEs.

hunt_mat
Homework Helper
The idea is basically to view the solution of the PDE as a surface $$u=u(x,y)$$ and the equation is in fact the dot product between the normal at that point and the tangent plane. You just integrate up the equations for the tangent plane basically.