Consider the system y' = Ay, where A = (alpha 2 -2 0) and alpha is a constant (a) Under what conditions will the system have a saddle at the origin? (b) Under what conditions will the system have an asymptotically stable node at the origin? (c) Under what conditions will the system have an asymptotically unstable node at the origin (d) Under what conditions will the system have an asymptotically stable spiral point at the origin? (e) Under what conditions will the system have an asymptotically unstable stable spiral point at the origin? (f) Under what conditions will the system have trajectories which are periodic, closed curves about the origin? (g) Under what conditions will the system have an improper node at the origin?
Show transcribed image text Consider the system y' = Ay, where A = (alpha 2 -2 0) and alpha is a constant (a) Under what conditions will the system have a saddle at the origin? (b) Under what conditions will the system have an asymptotically stable node at the origin? (c) Under what conditions will the system have an asymptotically unstable node at the origin (d) Under what conditions will the system have an asymptotically stable spiral point at the origin? (e) Under what conditions will the system have an asymptotically unstable stable spiral point at the origin? (f) Under what conditions will the system have trajectories which are periodic, closed curves about the origin? (g) Under what conditions will the system have an improper node at the origin?