{VERSION 2 3 "APPLE_68K_MAC" "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 1 116 111 127 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 112 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 150 0 172 0 0 0 0 0 0 0 0 0 0 }1 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 104 168 230 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 197 191 130 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "top_s11_3" {TEXT -1 25 "11.3 Numerical \+ Solutions" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Belmonte, Summer 1996" }}{PARA 0 "" 0 "" {TEXT -1 64 "These are the shaded gray examples whic h appear in Section 11.3." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "Here \+ " }{TEXT 256 6 "dsolve" }{TEXT -1 9 " returns " }{TEXT 257 4 "NULL" } {TEXT -1 45 ", signifying that no solution could be found." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "restart; eq3:=diff(y(t), t) + sin(y(t)^2) = 1;\ndsolve(\{eq3, y(0)=1\}, y(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$eq3G/,&-%%diffG6$-%\"yG6#%\"tGF-\"\"\"-%$sinG6#*$F*\"\"#F.F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "dsolve(\{eq3, y(0)=1\}, y(t) , numeric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#:6#%(rkf45_xG6'%\"iG%(r kf45_sG%)outpointG%#r1G%#r2G6#%aoCopyright~(c)~1993~by~the~University~ of~Waterloo.~All~rights~reserved.G6\"C&>8&-%&evalfG6#9$@$52-%$absG6#,$ F1!\"\"-F:6#,&&%,loc_controlG6#\"\"#\"\"\"F1F=4-%'memberG6$&FB6#\"\"'< *FD!\"#FEF=$FE\"\"!$FDFP$FNFP$F=FPC%>FB-%%copyG6#=F.6#;FE\"#EE\\[l;\"# 9FP\"#>FP\"#BFP\"\")\"&++$\"#;FP\"\"($FE!\"*\"#=FPFEFEFLFE\"#5FP\"#6FP FDFP\"\"$FP\"#CFP\"#8FPFfnFP\"#AFP\"#%'loc_y0G-FW6#=F.6#;FEFEE\\[l\"FEFO>%'l oc_y1G-FW6#=F.FipE\\[l!@$0F9FPC$>&FB6#FdoF1@%1%'DigitsG-%'evalhfG6#Fjq C$>8%-%*traperrorG6#-F\\r6#-%=dsolve/numeric_solnall_rkf45G6,%&loc_FG- %$varG6#FB-F[s6#Fep-F[s6#F]q-F[s6#%'loc_F1G-F[s6#%'loc_F2G-F[s6#%'loc_ F3G-F[s6#%'loc_F4G-F[s6#%'loc_F5G-F[s6#%)loc_workG@$/F`r%*lasterrorGC% >8'-%+searchtextG6$.F\\r-%(convertG6$-%#opG6$FE7#F`r%%nameG>8(-Fjt6$.% )hardwareGF]u@%50FhtFP0FfuFP-Fgr6,FirFBFepF]qFcsFfsFisF\\tF_tFbt-%&ERR ORG6#F`rF_v7$/%\"tGF5-%$seqG6$/&%$ordG6#,&8$FEFEFE&Fep6#F_w/F_wFjpF.6% FBFepF]q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "f:=dsolve(\{eq3 , y(0)=1\}, y(t), numeric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG: 6#%(rkf45_xG6'%\"iG%(rkf45_sG%)outpointG%#r1G%#r2G6#%aoCopyright~(c)~1 993~by~the~University~of~Waterloo.~All~rights~reserved.G6\"C&>8&-%&eva lfG6#9$@$52-%$absG6#,$F3!\"\"-F<6#,&&%,loc_controlG6#\"\"#\"\"\"F3F?4- %'memberG6$&FD6#\"\"'<*FF!\"#FGF?$FG\"\"!$FFFR$FPFR$F?FRC%>FD-%%copyG6 #=F06#;FG\"#EE\\[l;\"#9FR\"#>FR\"#BFR\"\")\"&++$\"#;FR\"\"($FG!\"*\"#= FRFGFGFNFG\"#5FR\"#6FRFFFR\"\"$FR\"#CFR\"#8FRFhnFR\"#AFR\"#%'loc_y0G-FY6#=F 06#;FGFGE\\[l\"FGFQ>%'loc_y1G-FY6#=F0F[qE\\[l!@$0F;FRC$>&FD6#FfoF3@%1% 'DigitsG-%'evalhfG6#F\\rC$>8%-%*traperrorG6#-F^r6#-%=dsolve/numeric_so lnall_rkf45G6,%&loc_FG-%$varG6#FD-F]s6#Fgp-F]s6#F_q-F]s6#%'loc_F1G-F]s 6#%'loc_F2G-F]s6#%'loc_F3G-F]s6#%'loc_F4G-F]s6#%'loc_F5G-F]s6#%)loc_wo rkG@$/Fbr%*lasterrorGC%>8'-%+searchtextG6$.F^r-%(convertG6$-%#opG6$FG7 #Fbr%%nameG>8(-F\\u6$.%)hardwareGF_u@%50FjtFR0FhuFR-Fir6,F[sFDFgpF_qFe sFhsF[tF^tFatFdt-%&ERRORG6#FbrFav7$/%\"tGF7-%$seqG6$/&%$ordG6#,&8$FGFG FG&Fgp6#Faw/FawF\\qF06%FDFgpF_q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f(0); f(0.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/%\"tG\"\"! /-%\"yG6#F%$\"\"\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/%\"tG$\"\"& !\"\"/-%\"yG6#F%$\"1 " 0 "" {MPLTEXT 1 0 41 "with(plots): odeplot(f, [t, y(t)], 0..4);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "6 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }