Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 30
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Question A 30 

A solution to the two component differential equation system is
The matrix has real entries. What is ? 
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 

Note that is a solution of where and are eigenvalue and eigenfunction of matrix 
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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Please rate my easiness! It's quick and helps everyone guide their studies. We first note that can be written as Using the hint, we have and So, they have to satisfy Let We then get
Therefore, and This implies that and We finally have
