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

Find the general solution of the given differential equation:

y'' + 9y = (t^2)(e^3t) + 6

2. Relevant equations

3. The attempt at a solution

I want to first find a particular solution using the method of undetermined coefficients, but I'm not sure what I should "guess" for the form of Y(t). I learned that if g(t) is some exponential function such as e^2t, then I should assume the form looks like Y(t) = Ae^2t, assuming no duplication with solution to the homogenous equation. This doesn't seem to be much harder, but the t^2 and the +6 is confusing me a bit. Any help for how I can get started? Thanks!

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# Solution to nonhomogenous DE using Method of Undetermined Coefficients

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