Oudskid 0 ded 1, B -5 cied -5 iefrlrl cd ® © fw (3 (sto), 1 cd – HP 48g Graphing Calculator User Manual
Page 232
Attention! The text in this document has been recognized automatically. To view the original document, you can use the "Original mode".
y" =
.5j/' +
,5y + M+1
Step 1:
Convert the equation into a first-order equation:
Example:
Solve this equation for tti(l) given that
y { Q ) =
0 and
l/'(0) = 0 («;(0) = [ 0 0 ]):
y
0
1
.5 .5
y
(.51+1)
Step 2.
Store the values in fw (
0
1
.5 .5
and c (
OUDSKID 0 dED 1
(B -5 CIED -5 iEFrlRl CD ® © FW (3 (STO)
SICED
0
fSPC)
1
(ENTER
1 CD
©
c
(STO"|
.jg Step 3:
Enter the equation and initial values, set the solution
variable to w, and solve for w{\:y.
f?»)fSOLVr| |T| UK
(3 (3 FW ® CD F' © ®
(30 .5 © © T C£) 1
ENTER
SOLVE
F-
'FW*W+C*<.5*T+D'
INOEP:
T
INIT:
0
FINftL:
1
SDLN:
Id
INIT:
[
0,„
FINULtP
TDL:.0001 STEP: Df
It
_ STIFF
PRESS SOLVE FDR FINAL SOLN VALUE
H^aiiiHiiiiiiiiMiiiiiiBaBiiiNtaRi^^
© T
(ENTER)
0
(ENTER)
1
(ENTER)
© W
(ENTER) QCLD
0 fSPCT) 0
(ENTER)
S0L
V
E
Press
to view the result vector, w;(l), [ ,718262064225
1.71826206422 ]. The first value is ?/(l), the second value is :?/'(l).
How accm-ate is the answer? The original equations are
y = e^-t-l
and
y' = t + y
Evaluating the equations at 1 and comparing the results you can see
there is an error of approximately 0.0000198, which is well within the
specified error tolerance of
0
.
0001
.
19-6 Differential Equations