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
    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?