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Simple NonHomogenous Differential Equation Question

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data
    y"' -9y" +18y" = 30ex. Does not matter what the initial conditions are for my question.


    2. Relevant equations
    N/A


    3. The attempt at a solution
    So I factored out the equation and got:
    r*(r2 - 9r + 18)
    Which gives roots r = 0, r = 3, r = 6.
    Which gives me the general solution:
    y(x) = C0*1 + C1e3x + C2e6x
    Is the above general solution correct?
    Next question I have is whether I solved for the yp correctly.
    yp = A*ex
    yp' = A*ex
    yp" = A*ex
    yp'" = A*ex
    which by plugging into the equation will give.
    A*ex - 9A*ex + 18A*ex = 30ex
    which gives 10A*ex = 30ex
    which gives A = 3.
    Which means my general solution should be.
    y(x) = y(x) = C0*1 + C1e3x + C2e6x +3*ex
    Is all this correct because I am trying to solve for the "C0, C1, etc." and I want to be absolutely sure that the base I am working with is correct and that my error is just a miscalculation with the initial conditions. Thanks.
     
  2. jcsd
  3. Nov 24, 2009 #2

    LCKurtz

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    At first glance it looks OK to me. But if you really want to be sure, all you have to do is substitute your general solution back in to the DE and see if it works.
     
  4. Nov 24, 2009 #3
    Hmm didn't think about substituting back into the original DE. Thanks a lot for the tip.
     
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