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Systems of Differential Eq (Undetermined Coefficients)

  1. Nov 10, 2014 #1
    Hello guys,

    I need help solving this problem.

    Find the particular solution using method of undetermined coefficients:

    X'=AX + F(t)

    A= [4 ,1/3] <-- 1st row
    [9 , 6] <-- 2nd row

    F(t) = [-e^t,e^t]

    The complementary function is Xc=c1[1,3]e^(3t) + c2[1,9]e^(7t)

    Any help would be greatly appreciated!
  2. jcsd
  3. Nov 10, 2014 #2
    Repost. Sorry if things aren't clear. Here are the given using latex

    A=\begin{pmatrix}4 & 1/3\\ 9 & 6\end{pmatrix}

    F(t)=\begin{pmatrix}-e^t\\ e^t\end{pmatrix}

    ##Xc=c1\begin{pmatrix}1\\ 3\end{pmatrix}e^3t + c2\begin{pmatrix} 1\\ 9\end{pmatrix}e^7t##

    I'm having trouble finding the particular solution for the problem because F(t) is in exponential form. Please teach me how to approach this problem
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