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I am having trouble when solving non-homogeneous DE's how to find the annihilator to find my particular solution.

For example, if you have a DE that equals 24x^2cos(x), how do I find something that will annihilate this? It seems to me no matter how many derivatives you take, you couldn't get this thing to be 0.

The annihilator is needed to find the particular solution, right? When using the method of undetermined coefficients, I will have issues finding my particular solution.

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# Annihilator operator

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