1550078481-Ordinary_Differential_Equations__Roberts_

514 Ordinary Differential Equations

EXAMPLE Graphing the Direction Field of the

Differential Equation y' = x - y

Use DIRFIELD to graph the direction field of the differential equation
y' = x -yon the rectangle R = {(x, y) I -5:::; x:::; 5 and - 5:::; y:::; 5}.

SOLUTION

We double click the CSODE icon and after the program selection screen
appears, we single click on the DIRFIELD button. In the highlighted box
after "f(x,y) = " we input x - y and press the Enter key.
[NOTES: The only variables that may appear in the definition of f(x, y)
are x, X, y, and Y. Any constant that contains a decimal point must contain
at le ast one digit after the decimal point.]
Since we wish to graph the direction field of the differential equation on the

rectangle R = { ( x, y) I - 5 :::; x :::; 5 and - 5 :::; y :::; 5}, which is the default

rectangle, we simply click the VERIFY XMIN, XMAX, YMIN, YMAX AND
PLOT button. This causes the screen shown in Figure A.11 to appear.

"' DIRFIELD l!iliJ£i

OIAFIELD plots the direction field of y' = f(K. y) inside the rectangle x = Xmin. x = Xmax. y = Ymin. and y = Ymax

Enter the function f[x. y) = x-y

Enter Xmin • I

Ymin

Xmin

Ymin ""

'

'

'

'

'

-5

' '

' '

'

• /

Xmax •

' '

' '

'

• / / /

OPTIONS

r. Same Function. New Xmin. Xmax. Ymin. Ymax

(' New function ~

' '

'

' ' / -

' '

/

' ' -

/ /

' ' -

/ /

/ /

' '

/ /

/

/

Xmax

Figure A. 11 Entering the Function f(x, y) and the Bounding Rectangle

into DIRFIELD