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^+...