Chapter 1.2, Problem 5P

Phase Line Diagrams. Problems $1$ through $7$ involve equations of the form $dy/dt=f(y)$. In each problem, sketch the graph of $f(y)$ versus $y$, determine the critical (equilibrium) points, and classify each one as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the $ty-$ plane.

$dy/dt=y^2(y+1)(y-3),-\infty <y_0<\infty$.