Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (c)
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Question B 04 (c) 

A model of love affairs is described by the following system of differential equations where and are, respectively, Romeo’s and Juliet’s amount of love for each other at time . (c) Express the general solution to the system in either real or complex form. 
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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 

The general solution to the system of linear first order differential equations of the form can be written as: for eigenvectors and eigenvalues of the matrix , with arbitrary constants . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since the eigenvectors are linearly independent, we know that the general solution can be written as: for eigenvectors and eigenvalues of the matrix , with arbitrary constants . From part b), we know the eigenvalues and eigenvectors for . So substituting in, we get that the general solution is: Answer: 
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