Consider the following systems. Determine the families of orbits for each system and sketch several orbits in the phase plane and classify them by their type (stable node, etc.).

a.

\[\begin{aligned} x^{\prime} & =3 x \\ y^{\prime} & =-2 y \end{aligned}\]

b.

\[\begin{aligned} x^{\prime} & =-y \\ y^{\prime} & =-5 x \end{aligned}\]

c.

\[\begin{aligned} x^{\prime} & =2 y \\ y^{\prime} & =-3 x \end{aligned}\]

d.

\[\begin{aligned} x^{\prime} & =x-y \\ y^{\prime} & =y \end{aligned}\]

e.

\[\begin{aligned} x^{\prime} & =2 x+3 y \\ y^{\prime} & =-3 x+2 y \end{aligned}\]