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We saw that in the nonlinear system of differential equations:

We saw that in the nonlinear system of differential equations:

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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We saw that in the nonlinear system of differential equations: the quantity 1 1 H (2, v) = 5 + - is constant along solution curves. One of the equilibria of this system is a saddle. What is the value of H at the saddle? Along any solution curve that asymptotically approaches the saddle, either in forward or backward time, the value of H must be the same as at the saddle. Find a point on each of the 3 solution curves, colored black in the plot above, that asymptotically approach the saddle in either backwards or forwards time or both. Answers are 2,y coordinates as a vector.
Transcribed Image Text:We saw that in the nonlinear system of differential equations: the quantity 1 1 H (2, v) = 5 + - is constant along solution curves. One of the equilibria of this system is a saddle. What is the value of H at the saddle? Along any solution curve that asymptotically approaches the saddle, either in forward or backward time, the value of H must be the same as at the saddle. Find a point on each of the 3 solution curves, colored black in the plot above, that asymptotically approach the saddle in either backwards or forwards time or both. Answers are 2,y coordinates as a vector.
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