# Starting out in pde

imranq

## 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

Homework Helper
Gold Member
Have you tried separation of variables?

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

imranq
what is the method of characteristics?

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.

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.