Use the energy integral lemma to show that every solution

Chapter 4, Problem 16E

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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.

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