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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 0 "" 0 "" {TEXT 
26 7 "Advice:" }{TEXT -1 38 " Picking out members of a solution set" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "When Map
le's various \"solve\" commands (including " }{MPLTEXT 0 21 5 "solve" 
}{TEXT -1 2 ", " }{MPLTEXT 0 21 6 "dsolve" }{TEXT -1 2 ", " }{MPLTEXT 
0 21 6 "fsolve" }{TEXT -1 2 ", " }{MPLTEXT 0 21 6 "isolve" }{TEXT -1 
2 ", " }{MPLTEXT 0 21 6 "msolve" }{TEXT -1 5 " and " }{MPLTEXT 0 21 6 
"rsolve" }{TEXT -1 120 ") return the values of more than one variable \+
or function, they generally do so in the form of a set of equations, e
.g. " }{XPPEDIT 18 0 "\{ x = 5, y = 4 \}" "6#<$/%\"xG\"\"&/%\"yG\"\"%
" }{TEXT -1 166 ".  As with any set, the order in which these occur is
 unpredictable.  In particular, if you save your worksheet and reload \+
it in another session, the answer that was " }{XPPEDIT 18 0 "\{x = 5, \+
y = 4\}" "6#<$/%\"xG\"\"&/%\"yG\"\"%" }{TEXT -1 28 " the first time ma
y well be " }{XPPEDIT 18 0 "\{y = 4, x = 5\}" "6#<$/%\"yG\"\"%/%\"xG\"
\"&" }{TEXT -1 207 " the next time.  Therefore it is dangerous to try \+
to extract the parts of a solution in a way that depends on the order \+
in which they are presented in the set.  Instead, the recommended meth
od is to use the " }{MPLTEXT 0 21 4 "subs" }{TEXT -1 9 " command." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "In the ca
se of the numerical solution of a differential equation (" }{MPLTEXT 
0 21 19 "dsolve(...,numeric)" }{TEXT -1 331 "), the default is to retu
rn a procedure whose output will be a list of values of the dependent \+
and independent variables.  If the dependent variables are specified a
s a list rather than a set, this list will have the independent variab
le followed by the dependent variables in the same order as in the lis
t.  Note that without the " }{MPLTEXT 0 21 7 "numeric" }{TEXT -1 105 "
 option, the dependent variables must be a set, not a list.  Still, th
e most convenient method is to use " }{MPLTEXT 0 21 4 "subs" }{TEXT 
-1 69 " to extract the value of the variable you want.  On the other h
and,  " }{MPLTEXT 0 21 42 "dsolve(..., numeric, output=listprocedure)
" }{TEXT -1 27 " returns a list from which " }{MPLTEXT 0 21 4 "subs" }
{TEXT -1 79 " extracts a procedure to calculate the value of each vari
able.  Alternatively, " }{MPLTEXT 0 21 32 "dsolve(..., numeric, values
=...)" }{TEXT -1 119 " returns a matrix with the values of the depende
nt variables at each of an array of values of the independent variable
." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 48 "solution:= solve(\{ x + y = 9, x - y = 1\},
\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)solutionG<$/%\"yG\"\"%
/%\"xG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "xvalue:= sub
s(solution,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xvalueG\"\"&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "xy:= subs(solution,[x,y]);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xyG7$\"\"&\"\"%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 30 "q:= subs(solution, x^2 + y^2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"qG\"#T" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "de:= \{D(x)(t)=x(t)+y(t), D(y)(t)=y(t), x(0)=1, y(0)=
1\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "desol1:= dsolve(de,
 \{x(t),y(t)\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'desol1G<$/-%\"
yG6#%\"tG-%$expGF)/-%\"xGF)*&F+\"\"\",&F*F1F1F1F1" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 35 "x1:= unapply(subs(desol1,x(t)), t);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1GR6#%\"tG6\"6$%)operatorG%&arrowG
F(*&-%$expG6#9$\"\"\",&F0F1F1F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "desol2:= dsolve(de, [x(t),y(t)],numeric);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%'desol2GR6#%(rkf45_xG6'%\"iG%(rkf45_sG%)ou
tpointG%#r1G%#r2G6#%aoCopyright~(c)~1993~by~the~University~of~Waterloo
.~All~rights~reserved.G6\"C&>8&-%&evalfG6#9$@$52-%$absG6#,$F3!\"\"-F<6
#,&&%,loc_controlG6#\"\"#\"\"\"F3F?4-%'memberG6$&FD6#\"\"'<*F?FG!\"#FF
$F?\"\"!$FPFR$FGFR$FFFRC%>FD-%%copyG6#=F06#;FG\"#LE\\[lBFGFFFFFR\"\"$F
R\"\"%$FG!\")\"\"&F\\oFNFG\"\"($FG!\"*\"\")\"&++$\"\"*\"%+5\"#5FR\"#6F
R\"#7FR\"#8FR\"#9FR\"#:FR\"#;FR\"#<FR\"#=FR\"#>FR\"#?FT\"#@FT\"#AFR\"#
BFR\"#CFR\"#DFR\"#EFR\"#FFR\"#GFR\"#HFR\"#IFR\"#JFR\"#KFRFhnFR>%'loc_y
0G-FY6#=F06#;FGFFE\\[l#FGFTFFFT>%'loc_y1G-FY6#=F0FbqE\\[l!@$0F;FRC$>&F
D6#FjnF3@%1%'DigitsG-%'evalhfG6#FcrC$>8%-%*traperrorG6#-Fer6#-%=dsolve
/numeric_solnall_rkf45G6,%&loc_FG-%$varG6#FD-Fds6#F^q-Fds6#Ffq-Fds6#%'
loc_F1G-Fds6#%'loc_F2G-Fds6#%'loc_F3G-Fds6#%'loc_F4G-Fds6#%'loc_F5G-Fd
s6#%)loc_workG@$/Fir%*lasterrorGC%>8'-%+searchtextG6$.Fer-%(convertG6$
-%#opG6$FG7#Fir%%nameG>8(-Fcu6$.%)hardwareGFfu@%50FauFR0F_vFR-F`s6,Fbs
FDF^qFfqF\\tF_tFbtFetFhtF[u-%&ERRORG6#FirFhv7$/%\"tGF7-%$seqG6$/&%$ord
G6#,&8$FGFGFG&F^q6#Fhw/FhwFcqF06%FDF^qFfqF0" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 10 "desol2(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/%
\"tG\"\"\"/-%\"xG6#F%$\"1BxzHOcOa!#:/-%\"yGF*$\"11f/D=G=FF-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(%, x(t));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"1BxzHOcOa!#:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "desol3:=dsolve(de,[x(t),y(t)],numeric,\n      output=
listprocedure);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'desol3G7%/%\"tGR
6#F'6\"6#%aoCopyright~(c)~1993~by~the~University~of~Waterloo.~All~righ
ts~reserved.GF*9$F*F*F*/-%\"xGF)RF)6&%(rkf45_sG%)outpointG%#r1G%#r2GF+
F*C&>8%-%&evalfG6#F-@$52-%$absG6#,$F9!\"\"-FA6#,&&%,loc_controlG6#\"\"
#\"\"\"F9FD4-%'memberG6$&FI6#\"\"'<*FDFL!\"#FK$FD\"\"!$FUFW$FLFW$FKFWC
%>FI-%%copyG6#=F*6#;FL\"#LE\\[lBFLFKFKFW\"\"$FW\"\"%$FL!\")\"\"&FaoFSF
L\"\"($FL!\"*\"\")\"&++$\"\"*\"%+5\"#5FW\"#6FW\"#7FW\"#8FW\"#9FW\"#:FW
\"#;FW\"#<FW\"#=FW\"#>FW\"#?FY\"#@FY\"#AFW\"#BFW\"#CFW\"#DFW\"#EFW\"#F
FW\"#GFW\"#HFW\"#IFW\"#JFW\"#KFWF]oFW>%'loc_y0G-Fhn6#=F*6#;FLFKE\\[l#F
LFYFKFY>%'loc_y1G-Fhn6#=F*FgqE\\[l!@$0F@FWC$>&FI6#F_oF9@%1%'DigitsG-%'
evalhfG6#FhrC$>8$-%*traperrorG6#-Fjr6#-%=dsolve/numeric_solnall_rkf45G
6,%&loc_FG-%$varG6#FI-Fis6#Fcq-Fis6#F[r-Fis6#%'loc_F1G-Fis6#%'loc_F2G-
Fis6#%'loc_F3G-Fis6#%'loc_F4G-Fis6#%'loc_F5G-Fis6#%)loc_workG@$/F^s%*l
asterrorGC%>8&-%+searchtextG6$.Fjr-%(convertG6$-%#opG6$FL7#F^s%%nameG>
8'-Fhu6$.%)hardwareGF[v@%50FfuFW0FdvFW-Fes6,FgsFIFcqF[rFatFdtFgtFjtF]u
F`u-%&ERRORG6#F^sF]w&Fcq6#FLF*6%FIFcqF[rF*/-%\"yGF)RF)F2F+F*C&>F9F:@$F
>C%>FI-Fhn6#=F*F[oE\\[lBFLFKFKFWF_oFWF`oFaoFcoFaoFSFLFdoFeoFgoFhoFioFj
oF[pFWF\\pFWF]pFWF^pFWF_pFWF`pFWFapFWFbpFWFcpFWFdpFWFepFYFfpFYFgpFWFhp
FWFipFWFjpFWF[qFWF\\qFWF]qFWF^qFWF_qFWF`qFWFaqFWF]oFW>Fcq-Fhn6#=F*FgqE
\\[l#FLFYFKFY>F[r-Fhn6#=F*FgqE\\[l!@$FarC$>FdrF9@%FgrC$>F^sF_s@$FbuC%>
FfuFgu>FdvFev@%FjvF]wF_wF]w&FcqFJF*FdwF*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "x3:= subs(desol3,x(t));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#x3GR6#%\"tG6&%(rkf45_sG%)outpointG%#r1G%#r2G6#%aoCopyright~(c
)~1993~by~the~University~of~Waterloo.~All~rights~reserved.G6\"C&>8%-%&
evalfG6#9$@$52-%$absG6#,$F2!\"\"-F;6#,&&%,loc_controlG6#\"\"#\"\"\"F2F
>4-%'memberG6$&FC6#\"\"'<*F>FF!\"#FE$F>\"\"!$FOFQ$FFFQ$FEFQC%>FC-%%cop
yG6#=F/6#;FF\"#LE\\[lBFFFEFEFQ\"\"$FQ\"\"%$FF!\")\"\"&F[oFMFF\"\"($FF!
\"*\"\")\"&++$\"\"*\"%+5\"#5FQ\"#6FQ\"#7FQ\"#8FQ\"#9FQ\"#:FQ\"#;FQ\"#<
FQ\"#=FQ\"#>FQ\"#?FS\"#@FS\"#AFQ\"#BFQ\"#CFQ\"#DFQ\"#EFQ\"#FFQ\"#GFQ\"
#HFQ\"#IFQ\"#JFQ\"#KFQFgnFQ>%'loc_y0G-FX6#=F/6#;FFFEE\\[l#FFFSFEFS>%'l
oc_y1G-FX6#=F/FaqE\\[l!@$0F:FQC$>&FC6#FinF2@%1%'DigitsG-%'evalhfG6#Fbr
C$>8$-%*traperrorG6#-Fdr6#-%=dsolve/numeric_solnall_rkf45G6,%&loc_FG-%
$varG6#FC-Fcs6#F]q-Fcs6#Feq-Fcs6#%'loc_F1G-Fcs6#%'loc_F2G-Fcs6#%'loc_F
3G-Fcs6#%'loc_F4G-Fcs6#%'loc_F5G-Fcs6#%)loc_workG@$/Fhr%*lasterrorGC%>
8&-%+searchtextG6$.Fdr-%(convertG6$-%#opG6$FF7#Fhr%%nameG>8'-Fbu6$.%)h
ardwareGFeu@%50F`uFQ0F^vFQ-F_s6,FasFCF]qFeqF[tF^tFatFdtFgtFjt-%&ERRORG
6#FhrFgv&F]q6#FFF/6%FCF]qFeqF/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 6 "x3(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"1BxzHOcOa!#:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "desol4:= dsolve(de,[x(t),y(t
)],numeric,\n      value=array([0,1,2]));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'desol4G-%'matrixG6#7$7#-%'vectorG6#7%%\"tG-%\"xG6#F.
-%\"yGF17#-F&6#7%7%\"\"!$\"\"\"F9F:7%F;$\"+IOcOa!\"*$\"+C=G=FF?7%\"\"#
$\"+3or;A!\")$\"+og0*Q(F?" }}}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "See
 also:" }{TEXT -1 1 " " }{HYPERLNK 17 "subs" 2 "subs" "" }{TEXT -1 2 "
, " }{HYPERLNK 17 "solve" 2 "solve" "" }{TEXT -1 2 ", " }{HYPERLNK 17 
"dsolve" 2 "dsolve" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "dsolve/numeric
" 2 "dsolve,numeric" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "fsolve" 2 "fso
lve" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "isolve" 2 "isolve" "" }{TEXT 
-1 2 ", " }{HYPERLNK 17 "msolve" 2 "msolve" "" }{TEXT -1 2 ", " }
{HYPERLNK 17 "rsolve" 2 "rsolve" "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 24 "Maple Advisor Database, " }
{TEXT -1 15 " R. Israel 1997" }}}}{MARK "3 0 0" 0 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }