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Homework Help: Undetermined Coefficient with repeated roots

  1. Feb 26, 2010 #1
    1. The problem statement, all variables and given/known data

    The problem is: y" + 2y' - 3y = x^2*e^x

    2. Relevant equations

    3. The attempt at a solution

    I know the roots are y1 = -3 and y2 = 1, becoming e^x.

    I'm not sure how to set my yp up though with the repeating e^x.

    My ideas are yp = x * (x^2*A*e^x) or x * (Ax^2 + Bx + C)e^x.

    I was also curious on the setup of a problem where yp = P(x)*e^ax* cos(bx).
  2. jcsd
  3. Feb 26, 2010 #2


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    Homework Helper

    since '1' is a root, the PI for ex is xex, and PI for x2 is Ax2+Bx+C, so put those 2 together

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