Problem 20E

In Problems 19–24, convert the given second-order equation into a first-order system by setting . Then find all the critical points in the -plane. Finally, sketch (by hand or software) the direction fields, and describe the stability of the critical points (i.e., compare with Figure 5.12).

Figure 5.12 Examples of different trajectory behaviors near critical point at origin

Solution :

Step 1 :

In this problem we have to find all the critical points in the plane and describe the stability of the critical points .

Given the differential equation is