The Differential Equation can be expressed as a system of first order equations ?

1x'''+1x''−9x'−9x=0

can be expressed as a system of first order equations by letting x1=x x2=x' x3=x''. The system has the form X'=AX where A has entries:

A11 = , A12 = , A13 =

A21 = , A22 = , A23 =

A31 = , A32 = , A33 =

1 Answer

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  • hfshaw
    Lv 7
    8 years ago
    Favorite Answer

    You have:

    x''' + x'' - 9x' - 9x = 0

    or, rearranging:

    x''' = -x'' + 9x' + 9x

    As the question suggests, let x1 = x, x2 = x' and x3 = x''

    Then

    x1' = x2

    x2' = x3

    x3' = 9x1 + 9x2 - x3

    In matrix notation, if X is the column vector [x1, x2, x3] then:

    X' = A*X

    where

    A =

    [0, 1, 0]

    [0, 0, 1]

    [9, 9, -1]

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