Suppose that a system of differential equations is given in the following form $$\frac{dy}{dx} = Ay(x) + b(x)$$ with $A$ a matrix. If $y(x)$ is a general solution, what is the difference between showing there is at least one periodic solution and showing that all solutions are periodic?
2026-04-04 02:18:41.1775269121
Difference between showing there is at least one periodic solution and showing that all solutions are periodic
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Assume there exists a periodic solution $y_1(x)$ and a non-periodic solution $y_2(x)$. Then the first statement is true and the second is false.
Or assume there is no solution at all. Then the first statement is false and the second is true.