Phase Planes

The phase planes activity allows you to plot a family of solutions to a system of two differential equations  x' = f(x,y) and y' = g(x,y).   The phase plane of a system gives a picture of how the solution y varies with respect to x which will allow you to see general trends and stability of the solutions. The slope of an arrow located at the point (x,y) is given by g(x,y)/f(x,y) and indicates the trajectory of a solution to the system through that point.  You can add solutions by tapping on a point within the graph   and the corresponding solutions x(t) and y(t) will appear in the small window in the lower left corner.  Watch an animation that traces the x(t) and y(t) solutions and the corresponding curve in the x-y plane. Enter your own system of equations or explore one of the preloaded systems.