Chapter 7.1, Problem 10P

For each of the systems in Problems $1$ through $18$:

(a) Find all the critical points (equilibrium solution).

(b) Use a computer to draw a direction field and phase portrait for the system.

(c) From the plot(s) in part (b), determine whether each critical point is asymptotically stable, stable, or unstable, and classify it as to type.

(d) Describe the basin of attraction for each asymptotically stable critical point.

$\frac{dx}{dt}=x-12y-x^2,\frac{dy}{dt}=\left(1+y\right)\left(1-x\right)$