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Trying to use variation of parameters

  1. Dec 8, 2008 #1
    Consider, x' = x + 3y^3
    y' = -3y

    I am trying to use the fundamental matrix, F(t), and 3y^3 as my g(t) in order to plug into the variation of parameters formula...

    Xp = F(t) * \integral{ F(t)^-1 * g(t) } ,

    Am I going about this the wrong way?

    I am trying to get something in a form that I recognize, like

    [tex] X' = \begin{pmatrix}1 & 0 \\ 0 & -3\end{pmatrix}

    \begin{pmatrix}C_1 \\ C_2\end{pmatrix}

    + \begin{pmatrix} 3y^3 \\ 0 \end{pmatrix}


    Can I make that work?
  2. jcsd
  3. Dec 9, 2008 #2


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    Homework Helper

    Um, what does variation of parameters got to do with this one? Your system of DE isn't linear to begin with; look at the DE for x'
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