Texas-instruments PLUS TI-89 User Manual download pdf (Page 213)

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101

196 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 196 of 26

For a general solution, use the following syntax. For a particular

solution, refer to Appendix A.

deSolve(

1stOr2ndOrderODE

independentVar

dependentVar

)

Using the logistic 1st-order differential equation from the example on

page 176, find the general solution for

with respect to

deSolve(y' = 1/1000 y

(100

y),t,y)

Before using

deSolve()

, clear any existing

and

variables.

Otherwise, an error occurs.

1. In the Home screen

92 Plus:

use

deSolve()

to find the

general solution.

2. Use the solution to define a function.

a. Press

to highlight the solution in the history area. Then

press

to autopaste it into the entry line.

b. Insert the

Define

instruction at the

beginning of the line.

Then press

3. For an initial condition

y=10

with

t=0

, use

solve()

to find

the

constant.

4. Evaluate the general solution

(

) with the constant

@1=9/100

to obtain the

particular solution shown.

You can also use

deSolve()

to solve this problem directly. Enter:

deSolve(y' = 1/1000 y

(100

y) and y(0)=10,t,y)

Example of the deSolve(

) Function

The

deSolve()

function lets you solve many 1st- and 2nd-

order ordinary differential equations exactly.

Example

Tip: For maximum

accuracy, use 1/1000

instead of .001. A floating-

point number can introduce

round-off errors.

Note: This example does

not involve graphing, so you

can use any

Graph

mode.

Tip: Press

to move to

the beginning of the entry

line.

Note: If you got a different

constant (@2, etc.), solve

for that constant.

For @, type

TI-89:

TI-92 Plus:

@1 represents a constant. You may

get a different constant (@2, etc.).

For ', type

Do not use implied multiplication between the

variable and parentheses. If you do, it will be

treated as a function call.

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Texas-instruments PLUS TI-89 User Manual Page 213

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