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Homework Help: Find particular solution third order Diff Eq

  1. Mar 29, 2012 #1
    1. The problem statement, all variables and given/known data

    y''' - y = e^x + 7

    2. Relevant equations

    3. The attempt at a solution

    I used y=Ae^x +B and then I multiplied by x^2 because y_c = c1 + c2 e^x + c3 e^(-x)

    the c1 and c2 e^x value repeat. Therefore I got: y= Ax^2 e^x + Bx^2

    I got A = 0 and A=1 which is wrong and B=0

    Any hints? do I need to add a Cx e^x and then multiply by x^2?
  2. jcsd
  3. Mar 29, 2012 #2


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    Homework Helper

    Your auxiliary equation would be r^3-1=0 which would lead to only one real root and two imaginary roots.

    Since e^x is on the right side, the particular integral for the e^x on the right would be xe^x.

    You will need to change your complementary solution y_c to reflect one real root and two imaginary roots.
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