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Math Help - Second order ODEs - inhomogeneous

  1. #1
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    Unhappy Second order ODEs - inhomogeneous

    Hi,

    I have a prblem with a question that I'm working on I've managed to get so far but not sure what my next step should be. I wonder if anyone could point me in the right direction?

    I've managed this so far:

    QUESTION: Find the general solution of:

    d^2 y/ d x^2 - 3dy/dx + 2y = 5 + 6e^7x

    Find auxiliary equation: m^2 - 3m + 2
    => (m-1) (m-2) = 0
    => m1 = 1, m2 = 2.

    Hence complimentary function is:

    Y(x) = Ae^x + Be^2x



    Not sure where to go from here. I'm okay with normal inhomogeneous equations but basically..... I hate exponentials lol

    Any help would be greatly appreciated! :P

    Cheers
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  2. #2
    Eater of Worlds
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    Chaneysville, PA
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    You're correct, the complementary function is C_{1}e^{x}+C_{2}e^{2x}

    To use Undetermined Coefficients, try y_{p}=A+Be^{7x}

    and it will work out.

    y''_{p}=49Be^{7x}, \;\ y'_{p}=7Be^{7x}

    Sub into the original DE, equate coefficients, and solve for A and B.
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  3. #3
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    Thanks for that, I think that helps a lot

    Cheers mate
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