Suppose that the equilibrium of this system occurs at uj = 2 and u What are the values of a and a2? (b) After a change of variables to the variable r(t), we are left with a homo neous system of differential equations. What is that homogeneous syst in terms of (t)? Ax

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27. Consider the system of differential equations,
-2
[8]-4368-9]
5
[u(t)]
(a) Suppose that the equilibrium of this system occurs at u₁ = 2 and u₂ = 1.
What are the values of a and a2
(b) After a change of variables to the variable r(t), we are left with a homoge-
neous system of differential equations. What is that homogeneous system
in terms of (t)?
(c) What is the solution to this system of differential equations assuming
u₁(0)= = 3 and u₂(0) = 4?
Transcribed Image Text:27. Consider the system of differential equations, -2 [8]-4368-9] 5 [u(t)] (a) Suppose that the equilibrium of this system occurs at u₁ = 2 and u₂ = 1. What are the values of a and a2 (b) After a change of variables to the variable r(t), we are left with a homoge- neous system of differential equations. What is that homogeneous system in terms of (t)? (c) What is the solution to this system of differential equations assuming u₁(0)= = 3 and u₂(0) = 4?
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