**Example:** Consider the first order system

**1.**- Graph the nullclines for this system.
**2.**- Insert direction field "arrows" at the nullclines
**3.**- Determine the general direction of the direction field in each of the regions cut out by the nullclines.
**4.**- Sketch possible phase portraits for the two initial conditions indicated by "dots" for as long as the phase portraits stay within the graph's frame.

**5.**- Find all the equilibrium points of the system.

**Answer:**

**1.**- The x-nullclines can be obtained by setting
*x*'=0, i.e.The y-nullclines can be obtained by setting

*y*'=0, i.e. - For
**2, 3, 4**, use the following graph:

**5.**- The equilibrium points of the system are the intersection points
of the x-nullclines and y-nullclines. Therefore,
we get
,

which yields

*x*=2 and . Hence, we have two equilibrium points.

**
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