Differential Equations Quiz
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SYSTEMS OF DIFFERENTIAL EQUATIONS
Question 1
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Consider the linear system
x
′
=
(
α
−
1
5
−
1
)
x
\mathbf{x}' = \begin{pmatrix} \alpha & -1 \\ 5 & -1 \end{pmatrix} \mathbf{x}
x
′
=
(
α
5
−
1
−
1
)
x
. For which range of the parameter
α
\alpha
α
is the origin an asymptotically stable spiral point?
A
α
<
1
\alpha < 1
α
<
1
B
−
1
−
2
5
<
α
<
−
1
+
2
5
-1 - 2\sqrt{5} < \alpha < -1 + 2\sqrt{5}
−
1
−
2
5
<
α
<
−
1
+
2
5
C
−
1
−
2
5
<
α
<
1
-1 - 2\sqrt{5} < \alpha < 1
−
1
−
2
5
<
α
<
1
D
α
<
−
1
−
2
5
\alpha < -1 - 2\sqrt{5}
α
<
−
1
−
2
5
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