Graphing A Second Order Differential Equation; Drawing The Phase Plane Of A Second Order Differential Equation - Casio ClassPad 330 User Manual

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 Phase 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
u 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] - [2nd (Phase Plane)] or the B toolbar button.
(3) Use the differential equation editor to input x ' = x , y ' = − y .
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Graphing a Second Order Differential Equation

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