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Math Help - Trajectories

  1. #1
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    Trajectories

    Graph the trajectories for each solution

    X=c1[1] e^-t + C2 [2] e^2t
    [2] [1]

    How do you do this? In brackets are the matrices. should be [1]/[2] 1 is first number in row and 2 is first number in the second row, etc.
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  2. #2
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    x_1=c_1e^{-t}+2c_2e^{2t}
    x_2=2c_1e^{-t}+c_2e^{2t}
    c_1 \: and \: c_2
    must be determined from initial conditions.
    You may graph
    x_1(t), \: x_2(t) \: or \: x_2(x_1).
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  3. #3
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    Quote Originally Posted by ur5pointos2slo View Post
    Graph the trajectories for each solution

    X=c1[1] e^-t + C2 [2] e^2t
    [2] [1]

    How do you do this? In brackets are the matrices. should be [1]/[2] 1 is first number in row and 2 is first number in the second row, etc.
    So X= C_1\begin{bmatrix}1 \\ 2\end{bmatrix}e^{-t}+ C_2\begin{bmatrix}2 \\ 2\end{bmatrix}e^{2t}.
    But what do you mean "for each solution"? This problem has an infinite number of solutions- one for every choice of C_1 and C_2. You can't graph all of them!
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