Solution Found!
In 19–24, convert the given second-order equation into a
Chapter 5, Problem 19E(choose chapter or problem)
In 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
Questions & Answers
QUESTION:
In 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
ANSWER:SOLUTIONStep 1We have to find the critical point of the differential equation