Consider a system of two linear first-order ordinary differential equations: y₁ = y2, y₂ = −9y₁. a) The corresponding eigenvalues are A₁ = 3, λ₂ = −3 b) The corresponding eigenvectors of this linear ODE system are II and III I and IV where I:U₂ = (3) 1 II:u₂ = III:u₁ = IV:u₁ = -3i 1 3i 3i -1 A₁ = 3i, λ₂ = -3i c) The phase portrait for this system of ODEs is Unstable focus with spiral out I and III Stable focus with spiral in ₁9, 1₂-9 I and III Stable node Centre
Consider a system of two linear first-order ordinary differential equations: y₁ = y2, y₂ = −9y₁. a) The corresponding eigenvalues are A₁ = 3, λ₂ = −3 b) The corresponding eigenvectors of this linear ODE system are II and III I and IV where I:U₂ = (3) 1 II:u₂ = III:u₁ = IV:u₁ = -3i 1 3i 3i -1 A₁ = 3i, λ₂ = -3i c) The phase portrait for this system of ODEs is Unstable focus with spiral out I and III Stable focus with spiral in ₁9, 1₂-9 I and III Stable node Centre
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![= y2,
Consider a system of two linear first-order ordinary differential equations: y₁
a) The corresponding eigenvalues are
A₁ = 3, 1₂ = −3
b) The corresponding eigenvectors of this linear ODE system are
I and IV
II and III
where
I:u₂ =
II:u₂
III:u₁
IV:u₁
(3₁)
(-3₁)
(3)
= (³1)
3i
3i
=
=
λ₁ = 3i, λ₂ = -3i
c) The phase portrait for this system of ODEs is
Unstable focus with spiral out
I and III
Stable focus with spiral in
y2 = -9y₁.
₁9, λ₂ = -9
I and III
Stable node
Centre](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d084809-1178-4503-9f07-a3e1167e0479%2F5fef42e8-89c3-4e24-aedf-f1d672f486f9%2Fasluksd_processed.png&w=3840&q=75)
Transcribed Image Text:= y2,
Consider a system of two linear first-order ordinary differential equations: y₁
a) The corresponding eigenvalues are
A₁ = 3, 1₂ = −3
b) The corresponding eigenvectors of this linear ODE system are
I and IV
II and III
where
I:u₂ =
II:u₂
III:u₁
IV:u₁
(3₁)
(-3₁)
(3)
= (³1)
3i
3i
=
=
λ₁ = 3i, λ₂ = -3i
c) The phase portrait for this system of ODEs is
Unstable focus with spiral out
I and III
Stable focus with spiral in
y2 = -9y₁.
₁9, λ₂ = -9
I and III
Stable node
Centre
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