Given the system of nonlinear differential equations x = (x−y)(x + y)y' = (2+x)(5 + y)1. Find all three critical points.2. Linearize the system about each critical point.3. Classify each critical point by discussing the zeros of the corresponding characteristic equation.You don't have to solve the characteristic equation.

The differential equations are as follows:

Answered: y' = (2+x)(5 + y) 1. Find all three…

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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y' = (2+x)(5 + y) 1. Find all three critical points. 2. Linearize the system about each critical point. 3. Classify each critical point by discussing the zeros of the corresponding characteristic equation. You don't have to solve the characteristic equation.