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    Autonomous ODE: non-uniqueness of solutions

    Homework Statement We have the autonomous ODE: \dot{x} = f(x), x \in \mathbb{R} first we define the following sets: E := \{f(x) = 0\} E^+ := \{f(x) > 0\} f(x) is continuous so E is a closed set and E^+ is an open set. x_0 \in (x_-,x_+) where (x_-,x_+) is the connected component of E^+...