14-4-1

Graphing an Nth-order Differential Equation

14-4 Graphing an Nth-order Differential Equation

This section explains how to graph the solution curve(s) for an nth order (higher order) differential equation based on specified initial conditions.

With this application, an nth order differential equation is input in the form of a set of multiple first order differential equations.

Inputting an Nth-order Differential Equation and Initial Conditions, and then Graphing the Solutions

You can use the procedure in this section to graph the solution curves of the Nth-order differential equation input on the [DiffEq] tab for given initial conditions.

Note

• For Nth-order differential equations, only solution curves are drawn.

Example: To specify the three initial conditions (xi, y1i, y2i) = (0, −1, 0), (0, 0, 0), (0, 1, 0) for the differential equation y’’ = x − y and graph its solution curves

uClassPad 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] - [Nth (No Field)] or the !toolbar button.

(3)Use the differential equation editor to input y’’ = x − y.

•Input y’’ = x − y by dividing it into two first order differential equations. If we let y1 = y and y2 = y’, we see that y1’ = y’ = y2 and y2’ = y’’ = x − y1.

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(4) Tap the [IC] tab to display the initial condition editor.

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