Separation of Variables

I understand why we use separation of variables, however what I don't underastand is how we know what to make as our separation constant depending on the problem we are trying to tackle. Can anyone provide any clarification as to how we will know what to make as our separation constant?

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Original post by Sulaiman Mamoun

I understand why we use separation of variables, however what I don't underastand is how we know what to make as our separation constant depending on the problem we are trying to tackle. Can anyone provide any clarification as to how we will know what to make as our separation constant?

Can you post an example? I presume its a pde youre referring to?

(edited 3 months ago)

Original post by Sulaiman Mamoun

I understand why we use separation of variables, however what I don't underastand is how we know what to make as our separation constant depending on the problem we are trying to tackle. Can anyone provide any clarification as to how we will know what to make as our separation constant?

As above, could you clarify?

I suspect you are perhaps confusing why we take this constant to be negative and other times not? If so, this is just for brevity. In many BVP contexts it turns out that our boundary conditions are not satisfied when this separation constant is positive, or zero, therefore we must have it negative. However, for more general problems you should not be starting with the negativity assumption.

(edited 3 months ago)

Separation of Variables

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