CSODE User's Guide 515[NOTE: If we had wanted to graph the direction field on a different rectan-
gle, we would have changed the values of Xmin, Xmax, Ymin, and Ymax that
needed to be changed by clicking in the box after the variable and entering
the desired value.)
At the upper right-hand side of the graph is a set of options. The option
Same Function, New Xmin, Xmax, Ymin, Ymax is selected. If you click
the OK button, the current graph will disappear and you will be able to
change any of the values of Xmin, Xmax, Ymin, Ymax you wish to change.
A second option is for you to click the New Function option and click the OK
button. This option begins DIRFIELD again. When you are finished using
the program DIRFIELD, click on the box in the upper right-hand corner of
the monitor with the X in it. This will cause the selection screen to appear
which will allow you to run a different program in CSODE or to exit CSODE.Using SOLVEIVPThe program SOLVEIVP will attempt to calculate and graph the solution
of the initial value problem y' = f(x, y); y(c) =don the interval [a , b] where
a :S: c :S: b. Numerical integration starts at c and proceeds toward b. Inte-
gration in this direction is terminated before b is reached, if any one of the
following three conditions occurs:(i) f(x, y) is undefined at some (x, y) which the computer has selected,(ii) the number of times the computer has evaluated f(x, y) exceeds 5000,(iii) the magnitude of y is very large (IYI :'.'.: 1025 ).Next, integration is restarted at c and proceeds toward a. Integration in this
direction is terminated before a is reached, if any one of the conditions (i),
(ii), or (iii) occurs. After integration is completed, you may graph the solution
on the monitor with or without the associated direction field, you may print
the solution on the monitor, you may solve another initial value problem with
the same differential equation or with a new differential equation, or you may
exit from SOLVEIVP to the program selection screen.The best way for us to illustrate how to use the program SOLVEIVP and
the typical output of the program is through the following examples. We
suggest that you run the program SOLVEIVP for each of these examples and
verify that you obtain the same results.