Starting Out with PDEs: Solving au_x + bu_y + cu = 0

[imranq]

Homework Statement

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

$$au_x+bu_y+cu=0$$

Homework Equations

The Attempt at a Solution

Dunno what to do with that last term

 

[fzero]

Have you tried separation of variables?

 

[hunt_mat]

This equation can be solved via the method of characteristics.

 

[imranq]

what is the method of characteristics?

 

[hunt_mat]

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]

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.