Texas Instruments TI-89, TI-92

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 ù(100 ìy)

or coupled 1st-order differential equations such as:

y1' = ëy1 + 0.1 ùy1 ùy2

y2' = 3 ùy2 ìy1 ùy2

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' = ëy1 + 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.

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.