# Trajectories

• May 5th 2010, 05:27 AM
ur5pointos2slo
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.
• May 6th 2010, 02:57 PM
zzzoak
$\displaystyle x_1=c_1e^{-t}+2c_2e^{2t}$
$\displaystyle x_2=2c_1e^{-t}+c_2e^{2t}$
$\displaystyle c_1 \: and \: c_2$
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 AM
HallsofIvy
Quote:

Originally Posted by ur5pointos2slo
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 $\displaystyle X= C_1\begin{bmatrix}1 \\ 2\end{bmatrix}e^{-t}+ C_2\begin{bmatrix}2 \\ 2\end{bmatrix}e^{2t}$.
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!