Consider the following dynamical system:

$3$

$$x x x $0,$ x R $$

$($i$)$ Compute the equilibrium states and study their stability

$($ii$)$ Compute exactly the orbits of the system in the phase plane. Then integrate numerically

using software $($e$.$g$.,$ Python, Matlab, Mathematica,...$)$ this dynamical system for two specific

sets of $($non$-$trivial$)$ initial conditions and compare them to the corresponding exact analytical

solutions.