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Differential Equations Method of Undetermined Coefficients

  1. Apr 1, 2014 #1
    1. The problem statement, all variables and given/known data
    consider y'' + 2y' - 3y = 1 + xe^x, find the particular solution

    3. The attempt at a solution
    f(x) = 1 + xe^x
    f'(x) =e^x + xe^x
    f''(x) = 2e^x + xe^x

    so it looks like my particular solution is going to have a constant term, an e^x term and an xe^x term,
    so I can write

    Particular Solution:
    y(x) = A + Be^x + Cxe^x

    and then differentiate this twice and plug into the original equation? Is this on the correct track? I ask because an online source says that I should have
    y(x) = A + Bxe^x + C(x^2)e^x

    can someone help me understand why I am wrong if I am wrong? Why have an (x^2)e^x but no e^x?
  2. jcsd
  3. Apr 1, 2014 #2


    User Avatar
    Gold Member

    Hi PsychonautQQ,
    You know the general solution to your equation is the sum of the solution to the homogenous problem and a particular solution to the non-homogenous problem.

    I would suggest first finding the homogenous solution and perhaps then your question will be resolved.
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