Wave equation, separation of variables and the Laplace transform

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Solving the wave equation using separation of variables and the Laplace transform can yield the same results, but this is not guaranteed in all cases. The methods may produce different outcomes depending on the specific problem and boundary conditions involved. It is essential to verify calculations to rule out errors that could lead to discrepancies. Understanding the conditions under which the methods diverge is crucial for accurate application. Exploring specific examples can clarify when the results align or differ.
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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