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Show that the equation ï +x+ɛx³ = 0 (ɛ > 0) with x(0) = a, x(0) = 0 has phase paths given by x² + x² + ½ ex¹ = (1 + ½ sa²)a². 4 Show that the origin is a centre. Are all phase paths closed, and hence all solutions periodic?

Show that the equation ï +x+ɛx³ = 0 (ɛ > 0) with x(0) = a, x(0) = 0 has phase paths given by x² + x² + ½ ex¹ = (1 + ½ sa²)a². 4 Show that the origin is a centre. Are all phase paths closed, and hence all solutions periodic?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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1.38 Show that the equation x + x + x³ = 0 (ɛ > 0) with x (0) = a, x(0) = 0 has phase paths given by x² + x² + ²√ £x ² = (1 + ¼ su² )a². Show that the origin is a centre. Are all phase paths closed, and hence all solutions periodic?
Transcribed Image Text:1.38 Show that the equation x + x + x³ = 0 (ɛ > 0) with x (0) = a, x(0) = 0 has phase paths given by x² + x² + ²√ £x ² = (1 + ¼ su² )a². Show that the origin is a centre. Are all phase paths closed, and hence all solutions periodic?
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