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## Homework Statement

Hi, I don't really understand separation of variables very well, and I was hoping to do get my mind more clear on the following question:

(Q) Use separation of variables to find all the separable solutions of the equation:

d²y/dt² -c²(d²y/dx²) + w²y = 0

where 'w' and c are constants.

## The Attempt at a Solution

I first started by saying the solution to this equation can be written as:

y = X(x)T(t)

so: X(d²T/dt²) - c²(d²X/dx²)T + w²XT

divide through by XT we get:

(1/T)d²T/dt² -(c²/X)(d²X/dx²) + w² = 0

What would be the next step? How can I find a solution from here?