(maxima.info)Introduction to drawdf

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54.1 Introduction to drawdf
===========================

The function 'drawdf' draws the direction field of a first-order
Ordinary Differential Equation (ODE) or a system of two autonomous
first-order ODE's.

   Since this is an additional package, in order to use it you must
first load it with 'load("drawdf")'.  Drawdf is built upon the 'draw'
package, which requires Gnuplot 4.2.

   To plot the direction field of a single ODE, the ODE must be written
in the form:
            dy
            -- = F(x,y)
            dx

   and the function <F> should be given as the argument for 'drawdf'.
If the independent and dependent variables are not <x>, and <y>, as in
the equation above, then those two variables should be named explicitly
in a list given as an argument to the drawdf command (see the examples).

   To plot the direction field of a set of two autonomous ODE's, they
must be written in the form
            dx             dy
            -- = G(x,y)    -- = F(x,y)
            dt             dt

   and the argument for 'drawdf' should be a list with the two functions
<G> and <F>, in that order; namely, the first expression in the list
will be taken to be the time derivative of the variable represented on
the horizontal axis, and the second expression will be the time
derivative of the variable represented on the vertical axis.  Those two
variables do not have to be <x> and <y>, but if they are not, then the
second argument given to drawdf must be another list naming the two
variables, first the one on the horizontal axis and then the one on the
vertical axis.

   If only one ODE is given, 'drawdf' will implicitly admit 'x=t', and
'G(x,y)=1', transforming the non-autonomous equation into a system of
two autonomous equations.