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Consider the pair of differential equations dx 1 dt dy Y, x² – y?. dt (a) Find all the equilibrium points of these equations. (b) Classify each equilibrium point of this non-linear system as far as possible by considering the Jacobian matrix.

Consider the pair of differential equations dx 1 dt dy Y, x² – y?. dt (a) Find all the equilibrium points of these equations. (b) Classify each equilibrium point of this non-linear system as far as possible by considering the Jacobian matrix.

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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Consider the pair of differential equations dx dy Y, = x² – y?. dt dt (a) Find all the equilibrium points of these equations. (b) Classify each equilibrium point of this non-linear system as far as possible by considering the Jacobian matrix.
Transcribed Image Text:Consider the pair of differential equations dx dy Y, = x² – y?. dt dt (a) Find all the equilibrium points of these equations. (b) Classify each equilibrium point of this non-linear system as far as possible by considering the Jacobian matrix.
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