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-3 -3 x' х. -k -3 || 3 (a) Solve the system for k= What are the eigenvalues of the 2° coeifficient matrix? r2 = Classify the equilibrium point at the origin as to type. Choose one▼ (b) Solve the system for k = 6. What are the eigenvalues of the coeifficient matrix? 12 = Classify the equilibrium point at the origin as to type. Choose one v (c) In parts (a) and (b), solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of k. r1 = r2 : || ||

-3 -3 x' х. -k -3 || 3 (a) Solve the system for k= What are the eigenvalues of the 2° coeifficient matrix? r2 = Classify the equilibrium point at the origin as to type. Choose one▼ (b) Solve the system for k = 6. What are the eigenvalues of the coeifficient matrix? 12 = Classify the equilibrium point at the origin as to type. Choose one v (c) In parts (a) and (b), solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of k. r1 = r2 : || ||

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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-3 -3 x' х. -k -3 || 3 (a) Solve the system for k= What are the eigenvalues of the 2° coeifficient matrix? r2 = Classify the equilibrium point at the origin as to type. Choose one▼ (b) Solve the system for k = 6. What are the eigenvalues of the coeifficient matrix? 12 = Classify the equilibrium point at the origin as to type. Choose one v (c) In parts (a) and (b), solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of k. r2 = ||
Transcribed Image Text:-3 -3 x' х. -k -3 || 3 (a) Solve the system for k= What are the eigenvalues of the 2° coeifficient matrix? r2 = Classify the equilibrium point at the origin as to type. Choose one▼ (b) Solve the system for k = 6. What are the eigenvalues of the coeifficient matrix? 12 = Classify the equilibrium point at the origin as to type. Choose one v (c) In parts (a) and (b), solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of k. r2 = ||
(c) In parts (a) and (b), solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of k. r2 3 and 6 where the transition 2 Determine the value of k between from one type of behavior to the other occurs. This value k is called a bifurcation value of this problem. Bifurcation Value =
Transcribed Image Text:(c) In parts (a) and (b), solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of k. r2 3 and 6 where the transition 2 Determine the value of k between from one type of behavior to the other occurs. This value k is called a bifurcation value of this problem. Bifurcation Value =
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