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Thread: Matrices and differential equations

  1. #1
    Junior Member
    Mar 2011

    Matrices and differential equations

    I'm a little stuck on this question, i need to work out the matrix A given the conditions, i have a picture of it here:

    How do i know what dimensions A would be or how to correctly deduce it? it could be 3x3, 2x3, 1x3??

    Thanks for any help
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Nov 2010
    Madrid, Spain

    Re: Matrices and differential equations

    Denoting $\displaystyle x_1=x,\;x_2=x',\;x_3=x''$ we have:

    $\displaystyle \begin{Bmatrix}x'_1=x_2\\x'_2=x_3\\x'_3=x'''=-x_1-tx_2-(\sin t)\;x_3\end{matrix}$

    So we can write:

    $\displaystyle \begin{bmatrix}{x'_1}\\{x'_2}\\{x'_3}\end{bmatrix} = \begin{bmatrix}{0}&{1}&{0}\\{0}&{0}&{1}\\{-1}&{-t}&{-\sin t}\end{bmatrix} \begin{bmatrix}{x_1}\\{x_2}\\{x_3}\end{bmatrix}$
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