Vector Fields and Flowlines

Flowlines, or integral curves of a vector field $\vec{v(x,y)}=<P(x,y),Q(x,y)>$ are solutions of the system of differential equations

$$\begin{eqnarray*} {\displaystyle \frac{dx}{dt}} & = & P(x(t),y(t)) \\ {\displaystyle \frac{dy}{dt}} & = & Q(x(t),y(t)) \\ \end{eqnarray*}$$

The programs DiffEq, Phase Plane in the folder MacMath 9.2 and Planar Vector Fields in the folder MacMath 9.6 can be used to draw the vector fields and their integral curves. (For DiffEq, Phase Plane, it is important to reduce the step size below its default to something more like .02.)