Texas Instruments TI-89 사용자 설명서

Differential Equation Graphing

425

Defining a System for Higher-Order Equations

In the Y= Editor, you must enter all differential equations as 1st-order equations. If you
have an nth-order equation, you must transform it into a system of n 1st-order equations.

Transforming an Equation into a 1st-Order System

A system of equations can be defined in various ways, but the following is a general
method.

1. Rewrite the original differential equation

as necessary.

a) Solve for the highest-ordered

derivative.

b) Express it in terms of y and t.

c) On the right side of the equation only,

substitute to eliminate any references
to derivative values.

Note:

To produce a 1st-order equation,

the right side must contain non-derivative
variables only.

y'' + y' + y = e

y'' = e