374 Section 1.5: Direction Fields Via Mathematica

Here is a way to get Mathematica to plot a direction field for the differential equation
dy
dx
=f(x,y)=
2
y
-
2
x
.
f[x_,y_]:=y^2-x^2
VectorPlot[{1,f[x,y]},{x,-2,2},{y,-2,2},VectorPoints20,VectorStyle{Arrowheads[0]},VectorScale{Tiny,Automatic,None}]