Science:Math Exam Resources/Courses/MATH307/December 2005/Question 06 (a)
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Question 06 (a)
Consider the differential equation
(a) For what values of is the system stable, neutrally stable or unstable?
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Science:Math Exam Resources/Courses/MATH307/December 2005/Question 06 (a)/Hint 1
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To determine if a system is stable, neutrally stable or unstable, look at the eigenvalue. A system is:
- stable if
- neutrally stable (or asymptotically stable) if
- unstable if any eigenvalue
stable if: ; this implies that
neutrally stable if . Since -1<0, this occurs for any
the system is never unstable because -1 <0