Solution Found!
Answer: In 19–24, convert the given second-order equation
Chapter 5, Problem 20E(choose chapter or problem)
In Problems 19-24, convert the given second-order equation into a first-order system by setting \(v=y^{\prime}\) Then find all the critical points in the yv-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).
\(\frac{d^{2} y}{d t^{2}}+y=0\)
Equation transcription:
Text transcription:
v=y^{prime}
frac{d^{2} y}{d t^{2}}+y=0
Questions & Answers
QUESTION:
In Problems 19-24, convert the given second-order equation into a first-order system by setting \(v=y^{\prime}\) Then find all the critical points in the yv-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).
\(\frac{d^{2} y}{d t^{2}}+y=0\)
Equation transcription:
Text transcription:
v=y^{prime}
frac{d^{2} y}{d t^{2}}+y=0
ANSWER: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