They say that a dynamic system is different from a static system in that it depends on its past (states). This fact is evident in a difference equation since it clearly shows that at each instant the state x(n) is a function of say x(n-1). However, to me, it is not evident in differential equations. Is it possible to show that a differential equation solution depends on its past values?
It is a great question. For clear explanations, kindly go through the
file that I attached.
Dear Mohan
Thanks a lot for your answer. It is fantastic!
My mistake in answering this question was that I always considered the “solution” of a differential equation. This solution just shows dependence on the initial value and to me it was not enough to make the declaration that the solution depends on the past of the system. You were clever to explain it by recourse to Picard–Lindelof formulation. It clearly shows that the solution is dependent not only to the initial value but also to all the previous values through an integral. Thanks for preparing the pdf file.
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