Science:Math Exam Resources/Courses/MATH215/December 2013/Question 01 (b)
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Question 01 (b) 

Find the form (but not the values of the coefficients!) of a particular solution of the nonhomogeneous ODE 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

First things first: what's the homogeneous solution? 
Hint 2 

Now that we know the forcing term is not appearing in the homogeneous solution, what sort of guess would you take for a forcing term that's a first degree polynomial times a sinusoidal function? 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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 need to find the homogeneous solution. The characteristic polynomial has roots and hence the homogeneous solution is a linear combination of and . No such terms appear in the forcing function. The forcing function is a degree one polynomial times a sinusoidal function. We thus would guess a particular solution of form . 