# Science:Math Exam Resources/Courses/MATH215/December 2013/Question 05 (b)

MATH215 December 2013
Other MATH215 Exams

### Question 05 (b)

Now find the general solution of the nonhomogenous system (with matrix $A$ as above):

${\vec {x}}'=A{\vec {x}}+\left[{\begin{array}{c}25e^{3t}\\0\end{array}}\right]$ Hint: to find a particular solution, you may use either the method of variation of parameters, or the method of undetermined coefficients; for the latter, try ${\vec {x}}_{p}(t)=\left[{\begin{array}{c}(at+b)e^{3t}\\(ct+d)e^{3t}\end{array}}\right]$ 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!

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