Chapter 5: Differential Equation Graph Application
128
u
To start a graph/curve trace
1. Draw a solution curve (pages 123 through 124) or function graph (page 127).
2. Tap
=
or [Analysis] - [Trace].
5-4
Graphing an Expression or Value by Dropping It into
the Differential Equation Graph Window
You can use the procedures in this section to graph an expression or value by dragging it from the eActivity
application window or the Main application window, and dropping it into the Differential Equation Graph window.
To draw this type of graph:
Drop this type of expression or value into the Differential Equation
Graph window:
Slope field
1st-order differential equation in the form of
y
’ =
f
(
x
,
y
)
Solution curve(s) of a 1st-
order differential equation
Matrix of initial conditions in the following form:
[[
x
1
,
y
(
x
1
)][
x
2
,
y
(
x
2
)] .... [
x
n
,
y
(
x
n
)]]
• Note that the Slope field should already be graphed on the Differential
Equation Graph window before the matrix is dropped in. If it isn’t, dropping
in the matrix will simply plot points at the coordinates indicated by each (
x
,
y
) pair.
• Regardless of whether or not the Slope field is already graphed, values
in the dropped in matrix will be registered to the [IC] tab of the Differential
Equation Editor.
Solution curve(s) of an
n
th-
order differential equation
1)
n
th-order differential equation such as
y
” +
y
’ +
y
= sin(
x
), followed by
2) Matrix of initial conditions in the following form:
[[
x
1
,
y
1(
x
1
)][
x
2
,
y
1(
x
2
)] .... [
x
n
,
y
1(
x
n
)]] or
[[
x
1
,
y
1(
x
1
),
y
2(
x
1
)][
x
2
,
y
1(
x
2
),
y
2(
x
2
)] .... [
x
n
,
y
1(
x
n
),
y
2(
x
n
)]]
f
(
x
) type function graph
Function in the form
y
=
f
(
x
)
0508
To drag the 1st-order differential equation
y
’ = exp(
x
) +
x
2
and then the initial condition matrix [0, 1] from
the eActivity application window to the Differential Equation Graph window, and graph the applicable
slope field and solution curve
0509
To drag the
n
th-order differential equation
y
” +
y
’ = exp(
x
) and then the initial condition matrix [[0, 1, 0]
[0, 2, 0]] from the eActivity application window to the Differential Equation Graph window, and graph the
applicable solution curves
Tip:
An
n
th-order differential equation of the form
f
(
y
’,
y
”…,
x
) dropped into the Differential Equation Graph window will
be treated as
f
(
y
’,
y
”…,
x
) = 0.
