Problem 1. Classify the stability of the fixed points of the following systems: this means
solving for their eigenvalues and eigenvectors and plotting the vector field in the phase plane.
In addition, if the eigenvectors are real, plot them in phase space.
a)
$ \dot{x} = x - y, $
$ \dot{y} = x + y, $
b)
$ \dot{x} = 5x + 2y, $
$ \dot{y} = -17x - 5y, $
c)
$ \dot{x} = 5x + 10y, $
$ \dot{y} = -x - y, $
d)
$ \dot{x} = -x, $
$ \dot{y} = -y $
e)
$ \dot{x} = 0, $
$ \dot{y} = -y, $
