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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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Science:Math Exam Resources/Courses/MATH307/December 2005/Question 06 (a)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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
and thus
stable if: ; this implies that neutrally stable if . Since 1<0, this occurs for any the system is never unstable because 1 <0 