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dx dt dy dt =-X y+x²° You will note from the phase portrait below that there is a saddle at (0,0), and that there must be a curve (called stable manifold) in the x-y plane which separates the phase plane into 2 regions: one where y(t) → +∞, the other where y(t) → →∞ as t → +∞. - 4 = ax² + bx³ + x² + (no constant or linear terms since the curve is tangent to the stable eigen vector at (0,0)). dy dt To compute that curve, assume y = Compute (don't forget the chain rule...), apply the DS equations and match the coefficients. Your answer should be given as y= = , a polynomial in x.

dx dt dy dt =-X y+x²° You will note from the phase portrait below that there is a saddle at (0,0), and that there must be a curve (called stable manifold) in the x-y plane which separates the phase plane into 2 regions: one where y(t) → +∞, the other where y(t) → →∞ as t → +∞. - 4 = ax² + bx³ + x² + (no constant or linear terms since the curve is tangent to the stable eigen vector at (0,0)). dy dt To compute that curve, assume y = Compute (don't forget the chain rule...), apply the DS equations and match the coefficients. Your answer should be given as y= = , a polynomial in x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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dx dt dy dt -X = y + x² * You will note from the phase portrait below that there is a saddle at (0,0), and that there must be a curve (called stable manifold) in the x-y plane which separates the phase plane into 2 regions: one where y(t) → +∞, the other where y(t) →→→∞ast → +∞. 0 3 ax² + bx³ + cx² + 4 To compute that curve, assume y = (no constant or linear terms since the curve is tangent to the stable eigen vector at (0,0)). dy dt Compute (don't forget the chain rule...), apply the DS equations and match the coefficients. Your answer should be given as y a polynomial in x. 9 ●
Transcribed Image Text:dx dt dy dt -X = y + x² * You will note from the phase portrait below that there is a saddle at (0,0), and that there must be a curve (called stable manifold) in the x-y plane which separates the phase plane into 2 regions: one where y(t) → +∞, the other where y(t) →→→∞ast → +∞. 0 3 ax² + bx³ + cx² + 4 To compute that curve, assume y = (no constant or linear terms since the curve is tangent to the stable eigen vector at (0,0)). dy dt Compute (don't forget the chain rule...), apply the DS equations and match the coefficients. Your answer should be given as y a polynomial in x. 9 ●
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