{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "2 D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "Help Heading" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {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 \}" "<$/%\"xG\"\"&/%\"yG\"\"%" } {TEXT -1 166 ". As with any set, the order in which these occur is un predictable. In particular, if you save your worksheet and reload it \+ in another session, the answer that was " }{XPPEDIT 18 0 "\{x = 5, y = 4\}" "<$/%\"xG\"\"&/%\"yG\"\"%" }{TEXT -1 28 " the first time may wel l be " }{XPPEDIT 18 0 "\{y = 4, x = 5\}" "<$/%\"yG\"\"%/%\"xG\"\"&" } {TEXT -1 207 " the next time. Therefore it is dangerous to try to ext ract the parts of a solution in a way that depends on the order in whi ch they are presented in the set. Instead, the recommended method is \+ to use the " }{MPLTEXT 0 21 4 "subs" }{TEXT -1 9 " command." }}{PARA 0 "" 0 "" {TEXT -1 66 "In the case of the numerical solution of a diff erential equation (" }{MPLTEXT 0 21 19 "dsolve(...,numeric)" }{TEXT -1 140 "), the default is to return a procedure whose output will be a list of values of the dependent and independent variables. You can t hen use " }{MPLTEXT 0 21 4 "subs" }{TEXT -1 69 " to extract the value \+ of the variable you want. On the other hand, " }{MPLTEXT 0 21 42 "ds olve(..., numeric, output=listprocedure)" }{TEXT -1 27 " returns a lis t from which " }{MPLTEXT 0 21 4 "subs" }{TEXT -1 79 " extracts a proce dure to calculate the value of each variable. Alternatively, " } {MPLTEXT 0 21 32 "dsolve(..., numeric, values=...)" }{TEXT -1 119 " re turns a matrix with the values of the dependent variables at each of a n array of values of the independent variable." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "solution:= solve(\{ x + y = 9, x - y = 1\},\{x,y\});" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)solutionG<$/%\"yG\"\"%/%\"xG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "xvalue:= subs(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-% $expGF)/-%\"xGF),&F+\"\"\"*&F*F1F+F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "x1:= unapply(subs(desol1,x(t)), t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G:6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%$expG6#9 $\"\"\"*&F0F1F-F1F1F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " desol2:= dsolve(de, [x(t),y(t)],numeric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'desol2G:6#%(rkf45_xG6'%\"iG%(rkf45_sG%)outpointG%#r1 G%#r2G6#%aoCopyright~(c)~1993~by~the~University~of~Waterloo.~All~right s~reserved.G6\"C&>8&-%&evalfG6#9$@$52-%$absG6#,$F3!\"\"-F<6#,&&%,loc_c ontrolG6#\"\"#\"\"\"F3F?4-%'memberG6$&FD6#\"\"'<*F?FG!\"#FF$FG\"\"!$FF FR$F?FR$FPFRC%>FD-%%copyG6#=F06#;FG\"#LE\\[lB\"#GFR\"\")\"&++$\"#JFR\" #>FR\"#IFR\"#DFRFhnFRFGFF\"\"&$FG!\")\"\"($FG!\"*\"#8FRFNFG\"#;FR\"\"% Fbo\"#:FR\"#5FR\"#CFR\"#@FQ\"#=FR\"#FFR\"#HFR\"#EFR\"\"*\"%+5\"#KFR\" \"$FR\"#7FR\"#BFR\"#9FR\"#AFR\"#6FR\"#?FQ\"#%'loc_y0G-FY6#=F06 #;FGFFE\\[l#FGFQFFFQ>%'loc_y1G-FY6#=F0FbqE\\[l!@$0F;FRC$>&FD6#FepF3@%1 %'DigitsG-%'evalhfG6#FcrC$>8%-%*traperrorG6#-Fer6#-%=dsolve/numeric_so lnall_rkf45G6,%&loc_FG-%$varG6#FD-Fds6#F^q-Fds6#Ffq-Fds6#%'loc_F1G-Fds 6#%'loc_F2G-Fds6#%'loc_F3G-Fds6#%'loc_F4G-Fds6#%'loc_F5G-Fds6#%)loc_wo rkG@$/Fir%*lasterrorGC%>8'-%+searchtextG6$.Fer-%(convertG6$-%#opG6$FG7 #Fir%%nameG>8(-Fcu6$.%)hardwareGFfu@%50FauFR0F_vFR-F`s6,FbsFDF^qFfqF\\ tF_tFbtFetFhtF[u-%&ERRORG6#FirFhv7$/%\"tGF7-%$seqG6$/&%$ordG6#,&8$FGFG FG&F^q6#Fhw/FhwFcqF06%FDF^qFfq" }}}{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#$\"1BxzHOcOa!#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "de sol3:=dsolve(de,[x(t),y(t)],numeric,\n output=listprocedure);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'desol3G7%/%\"tG:6#F'6\"6#%aoCopyrig ht~(c)~1993~by~the~University~of~Waterloo.~All~rights~reserved.GF*9$F* F*/-%\"xGF):F)6&%(rkf45_sG%)outpointG%#r1G%#r2GF+F*C&>8%-%&evalfG6#F-@ $52-%$absG6#,$F9!\"\"-FA6#,&&%,loc_controlG6#\"\"#\"\"\"F9FD4-%'member G6$&FI6#\"\"'<*FDFL!\"#FK$FL\"\"!$FKFW$FDFW$FUFWC%>FI-%%copyG6#=F*6#;F L\"#LE\\[lB\"\"&$FL!\")\"#EFW\"#DFW\"#;FW\"\"%F`o\"#GFWF]oFW\"#@FV\"#I FW\"#=FW\"#6FW\"#5FWFKFW\"#8FW\"#CFW\"#BFW\"#KFWFLFK\"#:FW\"\"$FW\"#FF W\"#AFW\"#HFWFSFL\"\"*\"%+5\"#?FV\"\")\"&++$\"#FW\"#7FW\" \"($FL!\"*\"#9FW>%'loc_y0G-Fhn6#=F*6#;FLFKE\\[l#FKFVFLFV>%'loc_y1G-Fhn 6#=F*FgqE\\[l!@$0F@FWC$>&FI6#FapF9@%1%'DigitsG-%'evalhfG6#FhrC$>8$-%*t raperrorG6#-Fjr6#-%=dsolve/numeric_solnall_rkf45G6,%&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%*lasterrorGC%>8&-%+sear chtextG6$.Fjr-%(convertG6$-%#opG6$FL7#F^s%%nameG>8'-Fhu6$.%)hardwareGF [v@%50FfuFW0FdvFW-Fes6,FgsFIFcqF[rFatFdtFgtFjtF]uF`u-%&ERRORG6#F^sF]w& Fcq6#FLF*6%FIFcqF[r/-%\"yGF):F)F2F+F*C&>F9F:@$F>C%>FI-Fhn6#=F*F[oE\\[l BF_oF`oFboFWFcoFWFdoFWFeoF`oFfoFWF]oFWFgoFVFhoFWFioFWFjoFWF[pFWFKFWF\\ pFWF]pFWF^pFWF_pFWFLFKF`pFWFapFWFbpFWFcpFWFdpFWFSFLFepFfpFgpFVFhpFipFj pFWF[qFWF\\qFWF]qFWF^qF_qFaqFW>Fcq-Fhn6#=F*FgqE\\[l#FKFVFLFV>F[r-Fhn6# =F*FgqE\\[l!@$FarC$>FdrF9@%FgrC$>F^sF_s@$FbuC%>FfuFgu>FdvFev@%FjvF]wF_ wF]w&FcqFJF*Fdw" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "x3:= sub s(lsol,x(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x3G:6#%\"tG6&%(rkf 45_sG%)outpointG%#r1G%#r2G6#%aoCopyright~(c)~1993~by~the~University~of ~Waterloo.~All~rights~reserved.G6\"C&>8%-%&evalfG6#9$@$52-%$absG6#,$F2 !\"\"-F;6#,&&%,loc_controlG6#\"\"#\"\"\"F2F>4-%'memberG6$&FC6#\"\"'<*F >FF!\"#FE$FF\"\"!$FEFQ$F>FQ$FOFQC%>FC-%%copyG6#=F/6#;FF\"#LE\\[lB\"#KF Q\"#HFQ\"\"$FQ\"#5FQ\"#JFQ\"#7FQFEFQ\"#@FP\"#FQ\"#EFQFFFE \"#;FQ\"#GFQ\"#BFQFgnFQFMFF\"#IFQ\"\"%$FF!\")\"#6FQ\"#AFQ\"#?FP\"#CFQ \"#8FQ\"#=FQ\"#DFQ\"\")\"&++$\"#:FQ\"#FFQ\"\"($FF!\"*\"\"&Fio\"\"*\"%+ 5>%'loc_y0G-FX6#=F/6#;FFFEE\\[l#FEFPFFFP>%'loc_y1G-FX6#=F/FaqE\\[l!@$0 F:FQC$>&FC6#F[oF2@%1%'DigitsG-%'evalhfG6#FbrC$>8$-%*traperrorG6#-Fdr6# -%=dsolve/numeric_solnall_rkf45G6,%&loc_FG-%$varG6#FC-Fcs6#F]q-Fcs6#Fe q-Fcs6#%'loc_F1G-Fcs6#%'loc_F2G-Fcs6#%'loc_F3G-Fcs6#%'loc_F4G-Fcs6#%'l oc_F5G-Fcs6#%)loc_workG@$/Fhr%*lasterrorGC%>8&-%+searchtextG6$.Fdr-%(c onvertG6$-%#opG6$FF7#Fhr%%nameG>8'-Fbu6$.%)hardwareGFeu@%50F`uFQ0F^vFQ -F_s6,FasFCF]qFeqF[tF^tFatFdtFgtFjt-%&ERRORG6#FhrFgv&F]q6#FFF/6%FCF]qF eq" }}}{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-%'MATRI XG6#7$7#-%'VECTORG6#7%%\"tG-%\"xG6#F.-%\"yGF17#-F&6#7%7%\"\"!$\"\"\"F9 F: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 "fsolve" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "isolve" 2 "isolve" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "m solve" 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 "2 7 0 0" 24 }{VIEWOPTS 1 1 0 1 1 1803 }