$(22$ points$)$

For the differential equation

$x^{}=x^3-2x^2-8x$

a$.$ Sketch the vector field on the real line. Then, find all fixed points & classify their stability.

b$.$ For the initial condition $x(0)=-5,$ describe the flow of the trajectory.

c$.$ For the initial condition $x(0)=-0\mathrm{.}5,$ describe the flow of the trajectory.

d$.$ For the initial condition $x(0)=3,$ describe the flow of the trajectory.

e$.$ For the initial condition $x(0)=4,$ describe the flow of the trajectory.