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

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Homework Help Overview

The discussion revolves around a partial differential equation (PDE) of the form au_x + bu_y + cu = 0. Participants are exploring initial understanding and approaches to solving this equation as they begin their PDE studies.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • One participant expresses uncertainty about handling the last term in the equation. Others suggest methods such as separation of variables and the method of characteristics, prompting questions about the latter's definition and application.

Discussion Status

The conversation is active, with participants sharing different methods and seeking clarification on concepts. Some guidance has been offered regarding the method of characteristics, although there is no explicit consensus on the best approach yet.

Contextual Notes

Participants are at the beginning stages of their PDE course, which may influence their familiarity with the concepts discussed. There is an indication that certain methods should be covered in their coursework.

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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
 
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Have you tried separation of variables?
 
This equation can be solved via the method of characteristics.
 
what is the method of characteristics?
 
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.
 
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.
 

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