Texas Instruments PLUS TI-89 - Manual (Page 213)

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
y with respect to t .
deSolve(y' = 1/1000 y щ (100 м y),t,y)
Before using deSolve() , clear any existing t and y variables.
Otherwise, an error occurs.
1. In the Home screen
TI - 89 : "
TI - 92 Plus: ¥ "
use deSolve() to find the
general solution.
2. Use the solution to define a function.
a. Press C 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 @1 constant.
4. Evaluate the general solution
( y ) 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 щ (100 м 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 2 A 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: 2 R
@1 represents a constant. You may
get a different constant (@2, etc.).
For ', type 2 È .
Do not use implied multiplication between the
variable and parentheses. If you do, it will be
treated as a function call.