66.1 Introduction to plotdf

The function plotdf creates a plot of the direction field (also called slope field) for a first-order Ordinary Differential Equation (ODE) or a system of two autonomous first-order ODE’s.

Plotdf requires Xmaxima. It can be used from the console or any other interface to Maxima, but the resulting file will be sent to Xmaxima for plotting. Please make sure you have installed Xmaxima before trying to use plotdf.

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 plotdf. 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 plotdf 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 plotdf 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 plotdf 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, plotdf will implicitly admit x=t, and G(x,y)=1, transforming the non-autonomous equation into a system of two autonomous equations.