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based on an earlier version of the Wolfram Language.
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EquationTrekker[eqn, x, {t, tmin, tmax}]
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 tmin to tmax.
EquationTrekker[eqns, {x, y}, {t, tmin, tmax}]
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.
reopens a graphical interface with the treks saved in the EquationTrekkerState object state.
  • If eqn is a single first order ODE, plots of x[t] versus t are displayed. If eqn is a single second order ODE, plots of x'[t] versus x[t] are displayed. If eqns consist of a system of two first order ODEs, plots of y[t] versus x[t] 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 tmin to tmax is displayed, with the coordinate associated with tmin displayed as a point and the coordinate associated with tmax displayed as an arrowhead.
  • Changing defaults for newly created treks may be accomplished by typing a value in the text field and clicking the _(GraphicsData[CompressedBitmap, eJx1k81rE1EUxU8+Rl10Kbjtxv/CtYrQpeA2FGmL37W7UleCgi4EUXBXLIIo]
                               xC8wePil) button.
  • EquationTrekker 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 EquationTrekker window
PlotRange{Automatic,{-1,1}}range of values to include
TrekParameters{}list of parameters and parameter ranges
TrekGeneratorDifferentialEquationTrekmethod used to generate treks
  • A valid setting for TrekParameters is a list of rules of the form param->range, where range consists of a starting value and a range, {v, {vmin, vmax}}. The range specification may also consist of a single value v, which is equivalent to {v, {0, 2v}}.
This is a simple example demonstrating how EquationTrekker operates:
Click for copyable input
A window similar to the one below will appear (but with an empty canvas). Click the canvas to add treks: