(c) Determine whether the following sets M C R are invariant, positively invariant, negatively invariant, or neither. Prove your statement. i. M = {0} ii. M = {2} iii. M = [0, 2] iv. M = (-2,2) v. M = (0, ∞)
(c) Determine whether the following sets M C R are invariant, positively invariant, negatively invariant, or neither. Prove your statement. i. M = {0} ii. M = {2} iii. M = [0, 2] iv. M = (-2,2) v. M = (0, ∞)
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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Transcribed Image Text:Consider the continuous-time dynamical system given by the ODE & = –x.
![(c) Determine whether the following sets M CR are invariant, positively invariant,
negatively invariant, or neither. Prove your statement.
i. M = {0}
ii. M = {2}
ii. М %—D [0, 2]
= [0, 2]
iv. M = (-2,2)
v. M%3D (0, о0)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad4d02b6-78f1-4c0a-a713-3b04a8400050%2Fb21b5b1c-1b06-4429-803b-c6e1e74f1152%2Fn3qifjm_processed.png&w=3840&q=75)
Transcribed Image Text:(c) Determine whether the following sets M CR are invariant, positively invariant,
negatively invariant, or neither. Prove your statement.
i. M = {0}
ii. M = {2}
ii. М %—D [0, 2]
= [0, 2]
iv. M = (-2,2)
v. M%3D (0, о0)
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