# Classical phonons

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The below picture is from my book's derivation on the equations describing waves in matter. But problem is: I don't understand the solution of the differential equation - or "difference" equation (whatever that is). How is it solved with the proposed solution? If I plug it in I don't get anything meaningful.

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• differential equation.png
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$$\gamma u_s = u_{s+1} + u_{s-1},$$