Solve the system

$\displaystyle \frac{dx}{dt} =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 1 -4 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 4 -7

$x$

with $x(0) =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 3 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 2

.

Give your solution in real form.
$x_1 =$ ,
$x_2 =$ .

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[Note-- you may want to view a phase plane plot (right click to open in a new window).]

If $y' = Ay$ is a differential equation, how would the solution curves behave?

A. The solution curves converge to different points.
B. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
C. All of the solution curves would run away from 0. (Unstable node)
D. All of the solutions curves would converge towards 0. (Stable node)

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