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14-2-1
Graphing a First Order Differential Equation
14-2 Graphing a First Order Differential Equation
This section explains how to input a first order differential equation and draw a slope field,
and how to graph the solution curve(s) of a first order differential equation based on given
initial conditions.
Inputting a First Order Differential Equation and Drawing a Slope Field
A slope field is the family of solutions of a single, first order differential equation of the form
y
’=
f
(
x
,
y
). It is a grid of solution lines where each line has the slope
y
’ for a given grid value of
x
and
y
. It is often referred to as a “slope field” or “direction field” because only the direction
of the field at any given point in known, not the magnitude.
Example: To input
y
’ =
y
2
−
x
and draw its slope field
S
ClassPad 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] - [1st (Slope Field)] or the
toolbar button.
(3) Press the
.
key to display the soft keyboard.
(4) Input
y
’ =
y
2
−
x
.
8Y
A
7
U