What does being maximal (non-continuable) say about a solution of a differential equation?
Do I understand it correctly that a solution of a differential equation can be called maximal if it is unique (so its domain is defined in such a way that there is only one unique solution on it)? What can we infer from knowing that a solution of a differential equation is maximal?
The question has been motivated by the following problem:
How many zeros does the maximal solution of the following initial value problem have on its domain?
$$y' = \frac{y}{\cos x}$$
$$y(0) = 2$$
The solution to this IVP that I've got: $y = 2(\sec x + \tan x)$