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System of Differential Equations : Find Equilibrium Points and Linearize

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Consider the attached system of differential equations.
x' = xy + x
y' = xy + y^2

a. Find the equilibrium points associated with this system.
b. Linearize the system about each of the equlibrium points you find in part a.

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Solution Summary

The equilibrium points of a system of differential equations are found and the system linearized about those points. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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The system of equations is

a) To find the equilibrium points, we set

From the first ...

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