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Well, I am interested which differential equations define real analytic functions on at least real positive numbers, and hence at first need to know which of them define infinitely differentiable functions (C^infinity).

Hi, I am interested to know whether a theory exists that allows to answer the following sort of question. Does a solution of initial value problem of second order differential equation is infinitely differentiable on the set of positive real numbers? For example, 1) the solution of...