This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 EQUATION TREKKER PACKAGE SYMBOL

# EquationTrekker

 opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the first or second order ordinary differential equation eqn for the function x with the independent variable t in the range to . opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the system of two first order ordinary differential equations eqns for the functions x and y. EquationTrekker[state] reopens a graphical interface with the treks saved in the EquationTrekkerState object state.
• If eqn is a single first order ODE, plots of versus t are displayed. If eqn is a single second order ODE, plots of versus are displayed. If eqns consist of a system of two first order ODEs, plots of versus are displayed.
• Treks are invoked by right-clicking a coordinate, which generates a trek that starts at the point specified by the mouse cursor.
• The initial position of a trek is highlighted in yellow, and by default corresponds to an initial condition specified at t=0. However, only the section of the trek from to is displayed, with the coordinate associated with displayed as a point and the coordinate associated with displayed as an arrowhead.
• Changing defaults for newly created treks may be accomplished by typing a value in the text field and clicking the button.
• generates a modal dialog, and the kernel is controlled by the graphical interface until the window is closed.
• When the window is closed, a list containing an EquationTrekkerState object and a graphic is returned. The EquationTrekkerState object contains all of the information necessary to reopen the window with the treks that were displayed when the window was closed.
• The following options can be given:
 ImageSize {400,400} absolute size of window PlotRange {Automatic,{-1,1}} range of values to include TrekParameters {} list of parameters and parameter ranges TrekGenerator DifferentialEquationTrek method used to generate treks
• A valid setting for TrekParameters is a list of rules of the form , where range consists of a starting value and a range, . The range specification may also consist of a single value v, which is equivalent to .
• The default setting TrekGenerator creates treks by following the path of the dependent variables generated using NDSolve.
• The setting TrekGenerator creates treks by sampling the phase space. The sampling interval is typically periodic.
This is a simple example demonstrating how operates:
A window similar to the one below will appear (but with an empty canvas). Click the canvas to add treks:
 Needs["EquationTrekker`"]This is a simple example demonstrating how operates:A window similar to the one below will appear (but with an empty canvas). Click the canvas to add treks:
 Options   (1)
This shows a nonlinear perturbation of the simple harmonic oscillator with sliders for and :