Wave equation, separation of variables and the Laplace transform

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Homework Help Overview

The discussion revolves around solving the wave equation using two different methods: separation of variables and the Laplace transform. Participants are exploring whether these methods yield the same results in all cases.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Some participants suggest trying both methods on an example to compare results. Others note that the outcomes can sometimes differ, prompting questions about the conditions under which this occurs.

Discussion Status

The discussion is ongoing, with participants questioning the reasons behind potential discrepancies between the two methods. There is an acknowledgment that more details may be necessary to clarify the situation.

Contextual Notes

Participants are considering the types of problems that may lead to different results when using the two methods, as well as the possibility of errors in calculations.

Johny911
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Homework Statement

Homework Equations


If i solve the wave equation using separation of variable and laplace tranform. Will i get the same answer ?

The Attempt at a Solution

 
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Johny911 said:

Homework Statement

Homework Equations


If i solve the wave equation using separation of variable and laplace tranform. Will i get the same answer ?

The Attempt at a Solution


Take an example. Try both methods. What do you get?
 
sometimes they are equal but sometimes they are not
 
Johny911 said:
sometimes they are equal but sometimes they are not

OK, so there's your answer.

But that just gets you started: why can they ever be unequal? What kind of problem gives you that? And: are you sure you have not made an error?

Maybe more details would be helpful.
 

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