Solve the system

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

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 1 -1 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 2 -1

$x$

with $x(0) =$

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

.

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

An ellipse with clockwise orientation An ellipse with counterclockwise orientation Spiral, spiraling outward in the clockwise direction Spiral, spiraling outward in the counterclockwise direction Spiral, spiraling inward in the clockwise direction Spiral, spiraling inward in the counterclockwise direction  1. Describe the trajectory.