For direction fields of ODE's of the form y' = f(x,y) set x'=1 in the first box above.

For example try x'=1 and y' = y-2*y^2. (Notice that you need to use * for all multiplications.) Or y' = x*y-2*y^2. (Don't use t, this equation plotter only understands variables named x and y. By setting x'=1 we have made the t variable and the x variable equal to each other.)

To change graphs you may need to hit the erase button a few times.

Caution -- the endpoints button for changing the scale may not work on older Macs using Netscape. Here is a fancier version of the phase plane plotter which may work better. Phase Plane Microscope

To plot the solution curves of a two dimensional system of autonomous differential equations, click on the box beside the x'(t) = label and enter an expression. The TAB key will cycle you through to the next field where you can enter the right hand side of the second equation. Click anywhere in the top window to select an initial condition.

The Endpoints button will open another panel where you can adjust the range of x and y that are displayed on the screen. You may also change the time interval over which the solution is computed. You will need to Erase the screen for the changes to take effect.

The Show/Hide Vectors button toggles the display of the vector field of the differential equation.

I.C. Grid starts 8 solution curves from a grid of initial conditions.

The parser recognizes all of the standard math functions defined in java.lang.Math. The symbols "E" and "PI" are recognized as java's Math.E and Math.PI.

The parser was written by Darius Bacon and is available at his web site. Please see his file on copying the software.

The java source for the rest of the applet was written by Scott Herod, last updated in January 1997. Copyright © 1997 by Scott A. Herod. All rights reserved.
The code was compiled for the U of R machine by Mike Gage.

The package uses a 4th order Runge-Kutta solver with a constant width mesh of 400 points, 200 from t = 0 to t = tmax and 200 from t = 0 to t = tmin.

Last updated: Thursday, April 13, 2000
http://www.math.rochester.edu/courses/current/MTH163/phaseplane.html