1. Write the ODE as a system by taking y1 =y and y2 = Consider the ODE y" - 9y + y* = 0. 2. Write the system as Y'= where Y = 3. Find all critical points of this system as (y1, Y2). 4. Linearize the system at any general point (y1-/2) as raf Y' = Dy 5. At each critical point (y1: 42), find the linearized system as Y' = AY where A is a 2x2 constant matrix and Y = 6. At each critical point, look at the corresponding A and find the type of the critical point, that is, if it is a node, saddle, spiral, or center.
1. Write the ODE as a system by taking y1 =y and y2 = Consider the ODE y" - 9y + y* = 0. 2. Write the system as Y'= where Y = 3. Find all critical points of this system as (y1, Y2). 4. Linearize the system at any general point (y1-/2) as raf Y' = Dy 5. At each critical point (y1: 42), find the linearized system as Y' = AY where A is a 2x2 constant matrix and Y = 6. At each critical point, look at the corresponding A and find the type of the critical point, that is, if it is a node, saddle, spiral, or center.
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
![1. Write the ODE as a system by taking y1 =y and
Consider the ODE
y" – 9y + y = 0.
Y2
= y1.
[Si(yn. 42)]
S2(y1, Y2)]
2. Write the system as Y' =
%3D
where Y =
3. Find all critical points of this system as (y1, 42)-
4. Linearize the system at any general point (y1. 2) as
rafi
Y' = Oy1
a12
AY where A is a 2x2 constant matrix
%3D
5. At each critical point (y1- Y2), find the linearized system as Y'
and Y =
Y2
6. At each critical point, look at the corresponding A and find the type of the critical point, that is, if it
is a node, saddle, spiral, or center.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe646156c-0bd7-48c6-bcbc-9d1619560090%2Fc209bdea-5af9-489f-b44e-ec0087b234ed%2Fihewp7g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Write the ODE as a system by taking y1 =y and
Consider the ODE
y" – 9y + y = 0.
Y2
= y1.
[Si(yn. 42)]
S2(y1, Y2)]
2. Write the system as Y' =
%3D
where Y =
3. Find all critical points of this system as (y1, 42)-
4. Linearize the system at any general point (y1. 2) as
rafi
Y' = Oy1
a12
AY where A is a 2x2 constant matrix
%3D
5. At each critical point (y1- Y2), find the linearized system as Y'
and Y =
Y2
6. At each critical point, look at the corresponding A and find the type of the critical point, that is, if it
is a node, saddle, spiral, or center.
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