I'm not sure how to deal with the $x$ and $e^x$ when multiplied together.
marked as duplicate by DonAntonio, Hurkyl, rschwieb, Henry T. Horton, Qiaochu Yuan Oct 20 '12 at 2:10
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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 $(c_1 x + c_2) x^k e^x$.