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Homogenous diff. equation and exponential matrix

  1. Sep 25, 2008 #1
    1. The problem statement, all variables and given/known data


    Given a matrix [tex]\left[\begin{array}{ccc}x_{11} & x_{12}\\x_{21} & x_{12}\end{array}\right][/tex]

    Which has the exponential matrix [tex]e^{t\cdot a}[/tex]

    When given the eqn [tex]x'= Ax + b[/tex] where [tex] b = \left[\begin{array}{c}b_1 \\ b_2\end{array}\right][/tex]

    I know that had it only been x' = Ax, then solution would be [tex]x = e^{ta} \cdot C[/tex] where C is a constant.

    Could someone here please be so kind to assist me in which secret formula do I use to expres the solution of the system x' = Ax+b??

  2. jcsd
  3. Sep 25, 2008 #2


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