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Math Help - Undet. Coefficients

  1. #1
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    Undet. Coefficients

    Using undetermined coefficients, find the gen. sol'n of the following Dif EQ:

    y'' + 4y' + 9y = 18t^2 + 1



    So, I'm not exactly sure how I'd do this. I was thinking of solving the homogenous part, and then the particular, but I think this is variation of parameters.
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  2. #2
    Senior Member tukeywilliams's Avatar
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     Y_{p}(t) = At^2 + Bt + C . Then differentiate. So  2A + 4 \left(2At + B \right) + 9 \left(At^2 + Bt + C \right) = 18t^2 + 1 . Expand out, write in decreasing powers, the solve for coefficients.
    Last edited by tukeywilliams; December 2nd 2007 at 07:39 PM.
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