When is it a good idea to assume solutions are separable?

[Issra]

When is it a good idea to assume solutions are separable? Are there any implied assumptions about the nature of the solutions when we assume that they are separable?

[Victor Ivrii]

If domain is "simple" in the appropriate coordinate system it is a good idea to try to find such solutions. For linear equations we even can construct general solutions as linear combinations of such solutions. Details in the class later.