Consider the system x ′ = y 3 − 4 x y ′ = y...

2nalfq8

2nalfq8

Answered

2022-07-02

Consider the system
x = y 3 4 x
y = y 3 y 3 x
What is the systemic way to find all the equilibrium points for this system?

Answer & Explanation

treccinair

treccinair

Expert

2022-07-03Added 18 answers

You should solve the system
y 3 4 x = 0 y 3 y 3 x = 0.
y 3 4 x = 0 y 3 y 3 x = 0.
From the first equation y 3 = 4 x, substituting into the second one you obtain 4 x y 3 x = 0, that is, x = y. Substituting back into the first equation you obtain
x 3 4 x = 0.
So x 1 = 0 , y 1 = 0, x 2 = 2 , y 2 = 2 and x 3 = 2 , y 3 = 2.

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