a11 a12 dx = Ax(t) where A = Consider a differential equation of the form The eigenvalues of A are complex conjugates. Analyze the stability of the equilibrium (0,0), and classify the equilibrium according to whether it is a a21 a22 stable spiral, an unstable spiral, or a center. The real part of the eigenvalues is V so the equilibrium is

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The real part of the eigenvalues is (negative, positive, zero) so the equilibrium is (a center, an unstable spiral, a stable spiral)

dx
a11 a12
Consider a differential equation of the form
= Ax(t) where A =
dt
The eigenvalues of A are complex conjugates. Analyze the stability of the equilibrium (0,0), and classify the equilibrium according to whether it is a
a21 a22
stable spiral, an unstable spiral, or a center.
- 7
4
A =
1
- 1
.....
The real part of the eigenvalues is
so the equilibrium is
Transcribed Image Text:dx a11 a12 Consider a differential equation of the form = Ax(t) where A = dt The eigenvalues of A are complex conjugates. Analyze the stability of the equilibrium (0,0), and classify the equilibrium according to whether it is a a21 a22 stable spiral, an unstable spiral, or a center. - 7 4 A = 1 - 1 ..... The real part of the eigenvalues is so the equilibrium is
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