20060301
14-3-1
Graphing a Second Order Differential Equation
14-3 Graphing a Second Order Differential
Equation
This section explains how to input a second order differential equation and draw a slope
field, and how to graph the solution curve(s) for a second order differential equation based
on given initial conditions.
With this application, a second order differential equation is input in the form of a set of two
first order differential equations.
Drawing the Pha
s
e Plane of a Second Order Differential Equation
A phase plane is the family of solutions of either a second order differential equation or two
first order differential equations of the form
x
’
=
dx
/
dt
=
f
(
x
,
y
) and
y
’
=
dy
/
dt
=
g
(
x
,
y
). A single
second order differential equation can also be graphed, but it must be written as two first
order differential equations.
Example:
To input {
x
’ =
x
,
y
’ = −
y
} and draw its phase plane
S
Cla
ss
Pad Operation
(1) On the application menu, tap
.
• This starts up the Differential Equation Graph application and activates the differential
equation editor ([DiffEq] tab).
(2) Tap [Type] - [2nd (Phase Plane)] or the
toolbar button.
(3) Use the differential equation editor to input
x
’ =
x
,
y
’ = −
y
.
7
U
8
U
Summary of Contents for ClassPad 330
Page 11: ...20060301 20090601 ClassPad 330 ClassPad OS Version 3 04 ...
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Page 779: ...20090601 S Graph Line Clustered C S Graph Line Stacked E 13 9 2 Graphing ...
Page 780: ...20090601 S Graph Line 100 Stacked F S Graph Column Clustered G 13 9 3 Graphing ...
Page 781: ...20090601 S Graph Column Stacked I S Graph Column 100 Stacked J 13 9 4 Graphing ...
Page 782: ...20090601 S Graph Bar Clustered K S Graph Bar Stacked 9 13 9 5 Graphing ...