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2nd order ODE with constant coefficients and tricky RHS

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data

    \frac {d^2x} {dt^2} -x = te^{-t}

    Find the general solution (I only need help on finding the particular solution).

    2. Relevant equations

    Well, I can easily find the complimentary solution via the characteristic equation, my problem lies in the particular solution.

    If the RHS (right hand side) is a simple exponential function, I know to guess [tex]Ae^{-t}[/tex] then take the derivatives and sub them back into the equation then solve for A. I also know if the RHS is a simple polynomial of t, I guess that the particular solution is of the form [tex]At^{n} + Bt^{n-1} + .... +[/tex].

    3. The attempt at a solution

    Given my above understanding, I tried guessing that the solution is [tex]Ate^{-t} + Bt[/tex] and [tex]Ate^{-t} + Be^{-t}[/tex] and both of them gave me no solution for B when trying to equate coefficients. So I have no idea what my guess should be.

    Any help? Thanks!
  2. jcsd
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