Hello Physics Forums, I sometimes come across statements like this (from here): Now assume a solution of the following form: x(t) = Aeat What is the motivation/background to make such an assumption? In this case the equation to be solved is x'' = 100x. Why would you assume the solution can usefully be written in that exponential form, or at all? Why does that type of step seem to be used so often? What is the role of A (a matrix I suppose...?) and a? Thanks!