Chapter 4.3, Problem 12P

In each of Problems 1 through 26:

(a) Find the general solution in terms of real functions.

(b) From the roots of the characteristics equation, determine whether each critical point of the corresponding dynamical system is asymptotically stable, stable, or unstable, and classify it as to type.

(c) Use the general solution obtained in part (a) to find a two parameter family of trajectories $X=x_{1}i+x_{2}j=yi+y\text{'}j$ of the corresponding dynamical system. Then sketch by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories.

$y\text{'}\text{'}+2y\text{'}+2y=0$