Let's say I have the equation(adsbygoogle = window.adsbygoogle || []).push({}); p(t)f''(t)=Kf(t)with p(t) a known periodical function, K an unknown constant and f(t) the unknown function.

This is an eigenvalues problem that once solved gives a set of K={k1, k2,...} eigenvalues.

I get these eigenvalues and they coincide with the ones obtained by others so I got them right.

Question

What if I try to solve the equation with a K that does not belong to the set of eigenvalues?

I have the initial conditions: f(0) and f'(0), I choose a K which is not an eigenvalue and I try to solve numerically the equation (using MATLAB):

What happens with f(t)? It is clear that I will get a solution. What is the difference between this solution with a forbidden K and a solution with an allowed K?

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# About an equation with eigenvalues

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