x = -2x+3y + xy y = -x+y=2xy²
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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Do all with explanation
Transcribed Image Text:1. In the following problems, show that each system has an equilibrium point at the origin. Com-
pute the Jacobian, then discuss the type and stability of the equilibrium point. Find and discuss
other equilibria if they exist.
(a)
(b)
(c)
-2x+3y + xy
y' = -x + y - 2xy²
x = x+y+ 2xy
= -2x+y+y³
x = -x + y²
=−x² + y²
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