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What can I guess as a particular solution for $y''+25y = -x\sin(5x)$

I tried $(Ax+B)(C\cos(5x)+Dsin(5x))$, but that didn't work.

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    That's the 5th (!) question by you within an hour or so, and they're all very similar. Please, just google for a table of common guesses for solutions of linear ODEs with various error terms2012-10-20
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    http://i.imgur.com/9OzUf.jpg2012-10-20
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    Here's one such table: http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients2012-10-20
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    That's what I used. I don't know why my solution is incorrect, though.2012-10-20
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    Then, at the very least, explain *what* didn't work. Put the actual equation you got for the coefficients into your question.2012-10-20
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    In the link @fpg provided you are considering the Qs and Rs to be the same (except for a multiplicative constant), and they aren't2012-10-20
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    So should I add the two instead of multiplying them?2012-10-20
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    Let me guess: B disappeared from the equation. Do you see why that is?2012-10-20
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    @fgp It's actually the sixth question in an hour! That's the 24 hour limit so OP is done for a while.2012-10-20

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We need to use something similar to the right hand side i.e. $${y_p} = Ax\sin (5x) + Bx\cos (5x).$$

Do you understand why?

If you do not understand why this is the way we guess, then try another but longer method. Take all the functions that appear in the product on the right hand side. Multiply them together and then simply put undetermined coefficients in from of each term.

If one of the functions is $\cos (ax)$ or $\sin (bx)$ then $\cos (ax) + \sin (bx)$ should appear in the product.

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    Suppose the right hand side were ${x^4}{e^{2x}}\cos (3x)$. What would be your guess?2012-10-20
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Here is a list of different combinations of functions for particular solutions.