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Is there an example of an autonomous ODE whose solution looks something like $\sin(1/x)$ near $x = 0$?

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I would say no, a solution for an autonomous ODE is monotone between two near singular points, and the limits are the singular points...also, $sin(1/x)$ is not $C^1$ near $0$(can someone verify this ? ODE is not my field) – Belgi May 22 '12 at 15:35

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