Euler’s Method For A Differential Equation With Two Input Variables - Texas Instruments TI-84 Plus Manual

Run the program. Each time the program stops for input or for
you to view a result, press
We choose to use 16 steps. Enter this value. The interval is 4
years, so enter the step size =
The initial condition is given as the
point (1, 53.2). Enter these values
when prompted for them.
Press
ENTER
obtain more estimates for total sales.
Record the input values and output
estimates on paper as the program
displays them.
When 16 steps have been completed
(that is, after the input reaches 5), the
program draws a graph of the points
(input, output estimate) connected
with line segments. This solution
graph is an estimate of the graph of
the differential equation solution.
Press turn
Y= ,
and press
ZOOM
draw the graph of the differential
equation.
EULER'S METHOD FOR A DIFFERENTIAL EQUATION WITH TWO INPUT
VARIABLES
from section 8.3. Follow the same process that is illustrated in the previous section of this
Guide, but enter
If the differential equation is written in terms of variables other than x and y, let the deriva-
tive symbol be your guide as to which variable corresponds to the input and which corresponds
to the output. For instance, if the rate of change of a quantity is given by
dy
dP
compare to
dx dn
The differential equation may be given in terms of y only. For instance, if
where k is a constant, enter
94
to continue.
ENTER
length of interval
number of steps
several more times to
off, turn on,
Plot3 Y1
to
▲ [Zoomfit]
We illustrate the use of Program
dy
in using the letters
Y1
dx
, entering in the expression
Y1
Y1 = K(30 – Y)
4
=
= 0.25.
16
with two variables using Example 2
EULER
and as they are written in the given equation.
x y
2
1.346Y(1 – X ).
. Of course, you need to store a value for k or substi-
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 8
The first application of
the formula gives an
estimate for the value
of the total sales at
x = 1.25:
S(1.25) ≈ 55.275
Continue pressing
to obtain
ENTER
more estimates of
points on the total
sales function S.
This is an estimate of the
graph of the function
S(t).
This is the slope graph –
the graph of S'(t).
= 1.346P(1 − n
dP
dn
Use to type
ALPHA 1 (Y)
dy
= k(30 – y)
dx
2
),
.
Y