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Cannot find nonhomogenous DE solution (should be easy?)

  1. Sep 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Determine the non-homogenous solution of the given differential equation.


    2. Relevant equations
    See 3.


    3. The attempt at a solution

    I have solved for the homogenous part, but as you can see in the link I am getting an unsolvable system of equations with the substitution method on the non-homogenous part. What am I doing wrong?

    Capture_zpsc57ed194.jpg
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 17, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You have to choose an other trial function for xp, as the inhomogeneous part contains the same exponent as one of the exponents in the homogeneous part.

    ehild
     
  4. Sep 18, 2013 #3

    pasmith

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    Homework Helper

    Try
    [tex]
    x_p = a\begin{pmatrix} 1 \\ -1 \end{pmatrix} te^{-t}
    + b\begin{pmatrix}1 \\ -5\end{pmatrix} e^{-t}
    [/tex]
     
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