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Choose the best answer. Consider the following statements regarding the equilibrium points of the system x' = x. 1. If a < 0, then 0 is a spiral sink. 2. The equilibrium 0 is stable for all values of a. 3. If a = 0, then 0 is a stable centre. 4. If a > 1, then 0 is an unstable saddle. 5. If 0 < a < 1, then 0 is an symptotically stable node. 6. If a = 1, then every point on the line x2 = -x1 is an equilibrium point, and all orbits are half-lines with slope 1. O Statements 1,2,4 and 6 are true. O Statements 2,3,5 and 6 are true. O Statements 1,3,4 and 5 are true. Statements 1,4,5 and 6 are true. O None of the above

Choose the best answer. Consider the following statements regarding the equilibrium points of the system x' = x. 1. If a < 0, then 0 is a spiral sink. 2. The equilibrium 0 is stable for all values of a. 3. If a = 0, then 0 is a stable centre. 4. If a > 1, then 0 is an unstable saddle. 5. If 0 < a < 1, then 0 is an symptotically stable node. 6. If a = 1, then every point on the line x2 = -x1 is an equilibrium point, and all orbits are half-lines with slope 1. O Statements 1,2,4 and 6 are true. O Statements 2,3,5 and 6 are true. O Statements 1,3,4 and 5 are true. Statements 1,4,5 and 6 are true. O None of the above

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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Choose the best answer. -1 -1 Consider the following statements regarding the equilibrium points of the system x' x. -a 1. If a < 0, then 0 is a spiral sink. 2. The equilibrium 0 is stable for all values of a. 3. If a = 0, then 0 is a stable centre. 4. If a > 1, then 0 is an unstable saddle. 5. If 0 < a < 1, then 0 is an symptotically stable node. 6. If a = 1, then every point on the line x2 =-x1 is an equilibrium point, and all orbits are half-lines with slope 1. O Statements 1,2,4 and 6 are true. Statements 2,3,5 and 6 are true. Statements 1,3,4 and 5 are true. Statements 1,4,5 and 6 are true. O None of the above
Transcribed Image Text:Choose the best answer. -1 -1 Consider the following statements regarding the equilibrium points of the system x' x. -a 1. If a < 0, then 0 is a spiral sink. 2. The equilibrium 0 is stable for all values of a. 3. If a = 0, then 0 is a stable centre. 4. If a > 1, then 0 is an unstable saddle. 5. If 0 < a < 1, then 0 is an symptotically stable node. 6. If a = 1, then every point on the line x2 =-x1 is an equilibrium point, and all orbits are half-lines with slope 1. O Statements 1,2,4 and 6 are true. Statements 2,3,5 and 6 are true. Statements 1,3,4 and 5 are true. Statements 1,4,5 and 6 are true. O None of the above
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