(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I've been having problems with a number of these things, here's the first one:

y'' -2y' -3y = -3te^{-t}

2. Relevant equations

I know that the general solution will be

y = y_{h}+ y_{p}

where y_{h}is the general solution to the homogeneous equation, and y_{p}

is the particular solution of the non-homogeneous equation.

3. The attempt at a solution

I got the homogeneous solutions very easily, but I'm tricked by how to solve for y_{p}. I understand the principle of the solution if the right side of the equation was simply -3e^{-t}, but when the extra t is thrown in there, my understanding breaks down.

I tried y_{p}=t^{2}e^{-t}, differentiated twice, and then input these expressions into the equation. I just realized that I was supposed to use an unknown coefficient (A we'll call it) with my guess at y_{p}. Since the terms on the right side are a product, will I just use A, or will I need some B as well? Thanks for any help.

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# Homework Help: Differential Equations - Method of Undetermined Coefficients

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