Texas-instruments PLUS TI-89 User Manual download pdf (Page 192)

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101

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

89 / TI

92 Plus

. Before using this chapter, you

should be familiar with Chapter 6: Basic Function Graphing.

The

89 / TI

92 Plus

solves 1st-order systems of ordinary

differential equations. For example:

y' = .001 y

(100

or coupled 1st-order differential equations such as:

y1' =

y1 + 0.1

y2' = 3

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' =

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

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.

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.

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