Lesson 33: differential equations, P: '1 .■■■■ < 1 +t''-2 ) -2*y-''2, Cd 1 © ai i sd © t [v – HP 48G User Manual
Page 95
Attention! The text in this document has been recognized automatically. To view the original document, you can use the "Original mode".
Lesson 33: Differential Equations
The
examples
in this lesson show you how to solve
an
initial-value
prolilem for a first-order differential equation and how to plot a phase
plane solution of a differential equation.
Example:
Find
y { t )
for
t
= 8 where
Y ' { T )
=
-
2 Y ~
and
y(0) = 0. Find the answer to within an error tolerance of
KFE
S t e p 1 :
Select
e d i
(ENTER)
in the SOLVE application.
Ш
F:
INDEP: X INIT: 0
FINflL:6.5
SDLN:
Y
INIT: 0
FINHL:
TDL:.0001 STEP:
Df It
_ STIFF
EHTEF; FUNCTION OF INDEP flND SPIN
S t e p 2 :
Enter the right hand expression (^ 2V'-) into F'. Notice
that the variables
appear
in
the menu
as
soon as
you
begin
the command
line,
so that
you can
use
them
as
typing aids.
CD 1 © ai i SD © T [V
2 ®
0
2 ® Y
(zD
2
(ENTER) (3 T (ENTER)
p:
' 1/(1+T2^'-2*Y'''2'
INDEP:
T
INIT:
Is—
FINF|L:F..
S
SDLN: V INIT: 0 FINAL:
TDL:.0001 STEP:
Df
It _ STIFF
ENTER INITIAL INDEP VAR VALUE
BiilTMMBBiMMMIIilll li) III I |l|l| I
S t e p 3 :
Check the remaining fields. You are using the default values
for the solution (Y) variable name as well as for the initial
values (0 and 0). You can use the default value for
(the
iterative
step
size) as
well. Change the final value
for
to 8, and the tolerance to 1E--7.
(© 8 (ENTER)
(T] 1 (EEX I
7
(V-1 (ENTER)
p:
'1
.■■■■
< 1
+T''-2
)
-2*Y-''2'
INDEP: X INIT: 0
FINAL: 8
SDLN:
Y
INIT: 0
FINAL:
TDL:.000,„ STEP: 1^03 _STIFF
ENTER INITIAL STEP SIZE
1МШ1
тжюзт
Calculus, Statistics and Advanced Mathematics 7-11