Chapter 9.6, Problem 9P

(a)

To determine

To show: That the origin is a stable critical point by using the given data.

(b)

To determine

To show: That the origin is asymptotically stable by using the given data.

(c)

To determine

To show: That the origin is a stable critical point using the given data.

(d)

To determine

To show: That $V\left(x,y\right)=\frac{1}{2}{\left(x+y\right)}^2+x^2+\frac{1}{2}{y}^2$ is a Liapunov function and conclude that the origin is an asymptotically stable using the given data.