**Problem (ST-2):** Find the critical points of the system below, and then use linearization to classify each one if possible. If it is not possible to classify a critical point this way, briefly explain why not.\[\frac{dx}{dt} = y(1-x-y)\]\[\frac{dy}{dt} = x(3-x-y)\]**Instructions:** 1. Identify the critical points of the given system of equations by setting \(\frac{dx}{dt} = 0\) and \(\frac{dy}{dt} = 0\).2. Use linearization to classify each critical point: - Linearize the equations around each critical point. - Determine the nature of each critical point using the Jacobian matrix and eigenvalues.3. If linearization does not allow classification, explain why it is not possible.

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Answered: (ST-2) Find the critical points of the…

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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(ST-2) Find the critical points of the system below, and then use linearization to classify each one if possible. If it is not possible to classify a critical point this way, briefly explain why not. dx dt dy dt || || y(1 - x - y) x(3 − x - y)