Solution Found!
Solved: In 19–24, convert the given second-order equation
Chapter 5, Problem 22E(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 1In this problem, we have to convert the second order to first order differential equation by setting and also we have to find the critical points in the plane.