Science:Math Exam Resources/Courses/MATH103/April 2015/Question 05 (b)
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Question 05 (b) 

Consider the differential equation . (b) Determine the stability of all steady states (equilibria). (Note: formal as well as graphical reasoning is acceptable.) 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
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 

For a differential equation of the form , the steady state is stable if . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the Hint , so , so at each steady state we check the sign of . At steady state we have so is unstable. At steady state we have so is stable. 