Answer
See below
Work Step by Step
We are given:
$x'=x(x-y+1)\\
y'=y(y+2x)$
To find equilibrium points, we take:
$0=x(x-y+1)\\
0=y(y+2x)$
Solving:
$(x,y)$$=(-1,0)\\
=(0,0)\\
=(-\frac{1}{3},\frac{2}{3})$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 9 - Systems of Differential Equations - 9.9 The Phase Plane for Linear Autonomous Systems - Problems - Page 653: 2
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