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Possible Duplicate:
Find a particular solution of the differential equation $-3y'‘-2y’+y=3xe^x$

I'm not sure how to deal with the $x$ and $e^x$ when multiplied together.

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    Uh? What's the question here?2012-10-19
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    What does the method of undetermined coefficients guess for $3xe^x$?2012-10-19
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    This 'question' is meaningless as it stands. Undetermined coefficients of what?2012-10-19
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    @user1038665 We don't know what you're looking at. We don't know what you mean by "guess". You really need to explain things like we were completely strangers. Oh, we are! =)2012-10-19
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    I'm not sure what you all mean. I'm referring to this: http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients If you look at the "Typical forms of the particular integral," I have the "function of x" as $3xe^x$ and I want to know the "form for y."2012-10-19
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    Well, what is your differential equation, to begin with? I see non in the question.2012-10-19
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    I'm just asking about $3xe^x$, why do you need to see a differential equation?2012-10-19
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    Because the method of "lucky guess" is for differential equations and, in fact, for non-homogeneous ordinary ones?! As it stands, the question is meaningless.2012-10-19
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    Looks like the user has made his revision by asking a new question: http://math.stackexchange.com/questions/217152/find-a-particular-solution-of-the-differential-equation-3y-2yy-3xex2012-10-20

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I'll assume you're talking about a differential equation $P(D) y = 3 x e^x$ where $P$ is a polynomial of degree $n$. If $P(1) \ne 0$, there will be a particular solution of the form $(c_1 x + c_2) e^x$ for some constants $c_1$ and $c_2$. If $1$ is a zero of $P$ of multiplicity $k$, then it will be $(c_1 x + c_2) x^k e^x$.