**DiffEqs `**DEGraphics

This package provides the following functions for plotting solutions of differential equations.

Plotting solutions of
differential equations.
**DEPlot**[*f*[*t,
y*], {*t*, *tmin*, *tmax*}, {*y*,
*ymin*, *ymax*}]
creates a plot showing the direction field and
solution curves for the differential equation *y*' =
*f*[*t, y*].**PhasePlot**[{*f*[*x,
y*], *g*[*x, y*]}, {*t*,
*tmin*, *tmax*}, {*x*, *xmin*,
*xmax*}, {*y*, *ymin*,
*ymax*}] creates
a plot showing the direction field and solution curves for
the autonomous system *x'* =
*f*[*x, y*], *y*' =
*g*[*x, y*].**PhasePlot**[{*f*[*t,
x, y*], *g*[*t, x, y*]}, {*t*,
*tmin*, *tmax*}, {*x*, *xmin*,
*xmax*}, {*y*, *ymin*,
*ymax*}] creates
a plot showing solution curves for the system
*x'* = *f*[*t, x, y*],
*y*' = *g*[*t, x, y*].**NDPlot**[*eqns*,
*fns*, {*t*, *tmin*, *tmax*}] uses
NDSolve to compute a numerical
solution of a system of (up to 3)
first-order differential equations and plots the
solution. Returns {*solution*, -Graphics-}.**PoincareTimeSection**[{*f*[*t,
x, y*], *g*[*t, x, y*]}, {*t*,
*t*_{0}, *tmax, dt*}, {*x*,
*x*_{0} }, {*y*, *y*_{0
}}] creates
a Poincaré time section plot of the solution
of *x'* = *f*[*t, x, y*],
*x*[*t*_{0}] =
*x*_{0}, *y*' = *g*[*t, x,
y*], *y*[*t*_{0}] =
*y*_{0}.**ViewProjections**[{*f*[*t*],
*g*[*t*], *h*[*t*]},
{*t*, *t*_{0}, *tmax*}, {*x, y,
z*}] creates a
GraphicsArray of projections of the curve
(*f*[*t*], *g*[*t*],
*h*[*t*]) onto the *xy*, *xz*,
and *yz* coordinate planes.**PlotImplicit**[*F*[*t,
y*], {*t*, *tmin*, *tmax*}, {*y*,
*ymin*, *ymax*}]
creates a contour plot of the function *F*.**TimeStatePlot**[{*x*[*t*],
*y*[*t*]}, {*t*, *tmin*,
*tmax*}, {*y*, *ymin*,
*ymax*}] creates a 3D
plot of the ``time-state trajectory" (*t*,
*x*[*t*], *y*[*t*]) with
projections onto the *t x*, *t y*, and *x y*
planes.

This loads the package.

`<<DiffEqs`DEGraphics``

**PoincareTimeSection
**

Here is an example of the use of PoincareTimeSection.

Options for PoincareTimeSection are the same as for ListPlot.

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**ViewProjections
**

Here is an example of the use of ViewProjections.

Options for ViewProjections are the same as for ParametricPlot and GraphicsArray with the addition of:

Options for ViewProjections.

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**TimeStatePlot
**

An example of the use of TimeStatePlot:

To plot the solution of a pair of differential equations, one must provide TimeStatePlot with the solution.

TimeStatePlot uses ParametricPlot3D and Shadow from the Graphics3D package. The options of ParametricPlot3D can be used, as well as the following:

Options for TimeStatePlot.

Here's an example in which several options are used.

If you specify PlotRange (e.g., when making an animation) , you'll need to make adjustments to the ShadowPositions.

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**PlotImplicit
**

Examples of the use of PlotImplicit:

PlotImplicit uses ContourPlot and DensityPlot and accepts any of their options. In addition, the following option can be used.

Options for PlotImplicit.

Converted by