184 Chapter 11: Differential Equation Graphing
11DIFFEQ.DOC TI-89/TI-92 Plus: Differential Equation (English) Susan Gullord Revised: 02/23/01 11:04 AM Printed: 02/23/01 2:15 PM Page 184 of 26
You can specify one or more initial conditions in the Y= Editor. To
specify more than one, enter them as a list enclosed in braces { } and
separated by commas.
To enter initial conditions for
the y1' equation, use the yi1 line,
etc.
For a 2nd- or higher-order differential equation, you must define a
system of 1st-order equations in the Y= Editor.
If you enter initial conditions,
you must enter the same number
of initial conditions for each
equation in the system.
Otherwise, a Dimension error
occurs.
If you do not enter initial conditions, the ncurves Window variable
( ¥$) specifies the number of solution curves graphed
automatically. By default, ncurves = 0. You can enter a value from
0 through 10. However, the Fields graph format and the Axes setting
determine whether ncurves is used.
If Fields = Then:
SLPFLD Uses ncurves, if not set to 0, to graph curves.
DIRFLD Ignores ncurves. Does not graph any curves.
FLDOFF Uses ncurves if Axes = TIME (or if Axes = Custom and
the x axis is t). Otherwise, a Diff Eq setup error occurs.
When ncurves is used, t0 is set temporarily at the middle of the Graph
screen. However, the value of t0 as set in the Y= Editor or Window
Editor is not changed.
Setting the Initial Conditions
You can enter initial conditions in the Y= Editor, let the
TI-89 / TI-92 Plus calculate initial conditions automatically, or
select them interactively from the Graph screen.
Entering Initial
Conditions in the
Y= Editor
Note: For information about
defining a system for higher-
order equations, refer to
page 186.
If You Do Not Enter
an Initial Condition
in the Y= Editor
Tip: Without entering initial
conditions, use
SLPFLD
(with
ncurves=0)
or
DIRFLD
to display a slope or
direction field only.
Note:
SLPFLD
is for a single
1st-order equation only.
DIRFLD
is for a 2nd-order
equation (or system of two
1st-order equations) only.
To graph a family of solutions,
enter a list of initial conditions.
To specify when the initial
conditions occur, use t0.
This is also the first t
evaluated for the graph.
Enter {10,20} even
though {10 20} is
displayed.