Solution Found!
Use the energy integral lemma to show that every solution
Chapter 4, Problem 16E(choose chapter or problem)
QUESTION:
Use the energy integral lemma to show that every solution to the Duffing equation (18) is bounded; that is, \(|y(t)| \leq M\) for some . [Hint: First argue that \(y^{2} / 2+y^{4} / 4 \leq K\) for some .]
Equation Transcription:
Text Transcription:
|y(t)|</=M
y^2/2+y^4/4</=K
Questions & Answers
QUESTION:
Use the energy integral lemma to show that every solution to the Duffing equation (18) is bounded; that is, \(|y(t)| \leq M\) for some . [Hint: First argue that \(y^{2} / 2+y^{4} / 4 \leq K\) for some .]
Equation Transcription:
Text Transcription:
|y(t)|</=M
y^2/2+y^4/4</=K
ANSWER:
Solution:
Step 1:
In this problem, we need to show that every solution of the given equation is bounded.