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Using laplace to solve 2 equationsplease check workthanks

  1. Mar 18, 2012 #1
    1. The problem statement, all variables and given/known data
    use laplace transforms to solve system of two equations
    x' = x -4y + e^4t
    y' = -x + y -4e^4t
    x(0) = 0
    y(0) =1


    2. Relevant equations
    i am uncertain about the correct order to solve these problems.. am I taking inverse L.T. at right time and place in order for the prob to check out? thanks for any help


    3. The attempt at a solution
    sX(s) - 0 - X(s) = -4Y(s) + 1/s-4
    X(s) = -4Y(s)/s-1 + 1/(s-4)(s-1)


    sY(s) -1 -Y(s) - 4Y(s)/s-1) = -1/(s-4)(s-1)
    Y(s) = 1/(s-1)(s-3)(s-4) + 1/s-3

    1 = A(s-1)(s-3) + B(s-4)(s-3) + C(s-4)(s-1)
    after letting s = 1, 3 and 4 i get
    A=1/3, B=1/6 and C=-1/2

    Y(s) = 1/3(1/s-4) + 1/6(1/s-1) -1/2(1/s-3)

    y(t) = (1/3)e^4t + (1/6)e^t - (1/2)e^3t

    y(t) = e^t

    X(s) = -4Y(s)(1/s-1) + 1/(s-4)(s-1)
    after using partial fractions on rightmost term on RHA and inserting y(t) for other term i get

    X(s) = -4e^t(1/s-1) + 1/(s-4)(s-1)

    x(t) = -4e^t(e^t) + (1/3)(1/s-4) - (1/3)(1/s-1)
    x(t) = -4e^t(e^t) + (1/3)e64t - (1/3)e^t


    final answer:
    x(t) = -4e^2t + (1/3)e^4t - (1/3)e^t
    y(t) = e^t
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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