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we know y(x) = (3sin(3x) + cos(3x))/40 satisfies y'' + 4y' + 13y = cos(3x), why don't we just plug that into y'' + 4y'

we know y(x) = (3sin(3x) + cos(3x))/40 satisfies y'' + 4y' + 13y = cos(3x), why don't we just plug that into y'' + 4y' + 13y = 40cos(3x) to find the particular solution

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