Science:Math Exam Resources/Courses/MATH152/April 2012/Question 08 (c)
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Question 08 (c) 

Consider the 2 x 2 system of differential equations where is the vector of unknown functions. Based on the results in (a) and (b), write down the general solution in realvalued form. 
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 

Remember that for any x. You can use this to decompose the solution into its real and imaginary parts. Since no imaginary component can be expressed in terms of the real components, the real and imaginary components can be used as a basis for the general solution. 
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. The complex solution that we found in (a) and (b) is From this we can read off the realvalued form as 