Science:Math Exam Resources/Courses/MATH215/December 2011/Question 07 (d)
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Question 07 (d) 

Consider the system of equations (d) Sketch the phase portrait of the nonlinear system. 
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 

First plot the neighbourhood of the critical points and use the results from 7c. Then fill in the remaining areas by calculating the derivative of the solution at exemplary points. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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