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Differential Equation, nonhomogeneous equation

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the general solution:
    y'' - y' - 2y = -2t + 4t^2


    2. Relevant equations



    3. The attempt at a solution

    r_1 = 2, r_2 = (-1)

    Set Y(t) = At^2 + B^t + C
    Y' = 2At + B
    Y'' = 2A

    2A - 2At + B - 2At^2 + Bt + C = -2t + 4t^2

    -2At^2 + (B-2A)t + 2A + B + C = -2t + 4t^2

    -2A = 4
    B - 2A = (-2)
    2A + B + C = 0

    The solution should have -2 = A, 3 = B, and -7/2 = C.
    But when I solve it, given the equations above, I don't get that. I only have A right.

    What's wrong?

    Thank you
     
  2. jcsd
  3. Oct 17, 2013 #2

    BruceW

    User Avatar
    Homework Helper

    The method is right, but there are several mistakes when you substitute into the equation. Maybe do this in a couple of steps, instead of one.
     
  4. Oct 17, 2013 #3
    Thanks
     
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