Exercise 101

Describe the behavior of the following systems without solving:

1. $x' = x + y$, $y' = x-y$.
2. $x_1' = x_1 + x_2$, $x_2' = 2 x_2$.
3. $x_1' = -2x_2$, $x_2' = 2 x_1$.
4. $x' = x + 3y$, $y' = -2x-4y$.
5. $x' = x - 4y$, $y' = -4x+y$.