Laplace transform for differential equations using State equations

Discussion in 'Homework Help' started by ukee1593, Feb 7, 2013.

  1. ukee1593

    Thread Starter New Member

    Jun 24, 2012
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    0
    Hi, I'm stuck getting the matrix for the laplace transform of the following differential equation:

    y''(t) + 7y'(t) + 9y(t) = z'(t) + 2z(t)

    So I start out with this by letting x1 = y(t), then x2 = x1' = y'(t) BUT the worked solutions for this question say that:

    x2(t) = x1'(t) - z = y'(t) - z ... y'(t) = x2(t) + z

    The problem is I cannot figure out WHERE that z comes from? I have never dealt with a differential like this before; all of the other examples are of the form:

    [2nd order ODE wrt y(t)] = z(t), could someone please explain how to separate this example up into the x1, x2, form?
     
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