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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- May 5th 2010, 05:27 AMur5pointos2sloTrajectories
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. - May 6th 2010, 02:57 PMzzzoak
$\displaystyle x_1=c_1e^{-t}+2c_2e^{2t}$

$\displaystyle x_2=2c_1e^{-t}+c_2e^{2t}$

$\displaystyle c_1 \: and \: c_2$

must be determined from initial conditions.

You may graph

$\displaystyle x_1(t), \: x_2(t) \: or \: x_2(x_1).$ - May 7th 2010, 03:52 AMHallsofIvy
So $\displaystyle X= C_1\begin{bmatrix}1 \\ 2\end{bmatrix}e^{-t}+ C_2\begin{bmatrix}2 \\ 2\end{bmatrix}e^{2t}$.

But what do you mean "for each solution"? This problem has an infinite number of solutions- one for every choice of $\displaystyle C_1$ and $\displaystyle C_2$. You can't graph all of them!