Example Of A 3Rd-Order Equation - Texas Instruments TI-89 Manual Book

Example of a 3rd-Order Equation

Example
Note: t0 is the time at which
the initial conditions occur.
By default, t0=0.
Important: For 3rd- or
higher-order equations, you
must set Fields= .
FLDOFF
Otherwise, an Undefined
variable error occurs when
graphing.
Note: With Axes= , the
TIME
solution to the selected
equation is plotted against
time (t).
Tip: To find the solution at a
particular time, use ... to
trace the graph.
For the 3rd-order differential equation y'''+2y''+2y'+y = sin(x),
write a system of equations to enter in the Y= Editor. Then
graph the solution as a function of time. Use initial conditions
y(0) = 0, y'(0) = 1, and y''(0) = 1.
1. Press 3 and set
2. Define a system of equations
for the 3rd-order equation as
described on page 186.
Rewrite the equation and
make the necessary
substitutions.
3. In the Y= Editor ( ¥ # ),
enter the system of
equations.
4. Enter the initial conditions:
, , and
yi1=0 yi2=1 yi3=1
5. Be sure that only y1'
selected. Use † to deselect
any other equations.
6. Press:
ƒ
9
or
— —
¥ Í
TI-89:
¥
TI-92 Plus: F
Set ,
Axes = ON Labels = ON
Solution Method = RK
= .
Fields FLDOFF
7. In the Y= Editor, press:
: 2 ‰
TI-89
TI-92 Plus: ‰
Set .
Axes = TIME
8. In the Window Editor
( ¥ $ ), set the
Window variables.
9. Display the Graph screen
( ¥ % ).
Chapter 11: Differential Equation Graphing
Graph=DIFF EQUATIONS
y''' + 2y'' + 2y' + y = sin(x)
y''' = sin(x) ì 2y'' ì 2y' ì y
y''' = sin(t) ì 2y'' ì 2y' ì y
y''' = sin(t) ì 2y3 ì 2y2 ì y1
y3' = sin(t) ì 2y3 ì 2y2 ì y1
Important: The solution to the y1'
is equation is the solution to the 3rd-
order equation.
,
, and
t0=0.
tmax=10.
tstep=.1
tplot=0.
.
xmin=ë 1. ncurves=0.
xmax=10. diftol=.001
xscl=1.
ymin=ë 3.
ymax=3.
yscl=1.
189