Texas Instruments PLUS TI-89 - Manual (Page 192)

Chapter 11: Differential Equation Graphing 175
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 175 of 26
Chapter 11:
Differential Equation Graphing
Preview of Differential Equation Graphing ........................................ 176
Overview of Steps in Graphing Differential Equations..................... 178
Differences in Diff Equations and Function Graphing...................... 179
Setting the Initial Conditions ................................................................ 184
Defining a System for Higher-Order Equations ................................. 186
Example of a 2nd-Order Equation ....................................................... 187
Example of a 3rd-Order Equation ........................................................ 189
Setting Axes for Time or Custom Plots ............................................... 190
Example of Time and Custom Axes .................................................... 191
Example Comparison of RK and Euler ............................................... 193
Example of the deSolve( ) Function.................................................... 196
Troubleshooting with the Fields Graph Format ................................ 197
This chapter describes how to solve differential equations
graphically on the
TI -89 / TI-92 Plus . Before using this chapter, you
should be familiar with Chapter 6: Basic Function Graphing.
The TI -89 / TI-92 Plus solves 1st-order systems of ordinary
differential equations. For example:
y' = .001 y щ (100 м y)
or coupled 1st-order differential equations such as:
y1' = ë y1 + 0.1 ù y1 ù y2
y2' = 3 ù y2 ì y1 ù y2
You can solve higher-order equations by defining them as a
system of 1st-order equations. For example:
y'' + y = sin(t) can be defined as y1' = y2
y2' =
ë y1 + sin(t)
By setting appropriate initial conditions, you can graph a
particular solution curve of a differential equation.
You can also graph a slope
or direction field that helps
you visualize the behavior of
the entire family of solution
curves.
For graphing, the TI -89 / TI-92 Plus uses numerical methods that
approximate the true solutions. The deSolve() function lets you
solve some differential equations symbolically. This chapter
introduces
deSolve() . Refer to Appendix A for more details.
11
Note: A differential equation
is:
• 1st-order when only
1st-order derivatives
appear.
• Ordinary when all the
derivatives are with
respect to the same
independent variable.