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Math Help - differential equation

  1. #1
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    differential equation

    very urgent!! help me please><!
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    1,458
    Hi

    You can use matrices.

    If X is the vector (x,y) then the equation is
    \dot{X} = A X

    where A is the matrix with -1 and 6 in the first row, and -1 and 4 in the second row

    This matrix is diagonalisable since its eigenvalues are 1 and 2
    The diagonal matrix is D with 1 ; 0 in the first row and 0 ; 2 in the second row
    Then you can find the matrix P such that P^{-1}AP = D

    If Y = P^{-1}X
    Then the initial equation becomes \dot{Y}=DY which can be easily solved

    Then you can find X by X = PY
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