Hi, I dont 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?