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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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