**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``

**PhasePlot
**

Here is an example of the use of PhasePlot, with the default value of InitialPoints. The system is .

No direction field is drawn if the vector
field depends on *t*.

This uses the Fitzhugh-Nagumo equations and a single initial point.

Options for PhasePlot are the same as for DEPlot, except that Isoclines is replaced by ShowNullclines.

Options for `PhasePlot`.

One more nice example:

Top

**NDPlot **

Here are three examples of the use of NDPlot.

Any of the options for NDSolve, Plot, ParametricPlot, or ParametricPlot3D can be used in NDPlot.

Converted by