{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 "" -1 259 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Tit le" 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_2" {TEXT -1 22 "11.2 Direction \+ Fields" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Belmonte, Summer 1996" }} {PARA 0 "" 0 "" {TEXT -1 65 "These are the shaded gray examples which \+ appear in Section 11.2. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT 260 5 "NOTE!" }{TEXT -1 5 " The " }{TEXT 259 7 "DEtools" }{TEXT -1 144 " package has been rewritten and expanded for Maple V Re lease 4. To find out more, select Help -> Contents -> What's New -> Sy mbolics -> DEtools." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart; with(DEtools);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#73%)DEnormalG%'DEplotG%)DEplot3dG%+DchangevarG%0PDEc hangecoordsG%(PDEplotG%+autonomousG%+convertAlgG%+convertsysG%+dfieldp lotG%+indicialeqG%.phaseportraitG%,reduceOrderG%*regularspG%*translate G%,untranslateG%)varparamG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "One thing which has changed in Release 4 is the syntax of the " }{TEXT 261 10 "dfieldplot" }{TEXT -1 28 " command. For details, type " } {TEXT 262 11 "?dfieldplot" }{TEXT -1 19 " at a Maple prompt." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "dfieldplot(diff(y(x), x) = x*sin(y(x)), y (x), x=-2..2, y=-1..1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Here i s way (different from that originally given in " }{TEXT 263 21 "CalcLa bs with Maple V" }{TEXT -1 131 ") to plot a solution curve on top of t he direction field for the preceding differential equation. It is pref erable for two reasons:" }}{PARA 0 "" 0 "" {TEXT -1 44 " 1. It use s one command instead of five." }}{PARA 0 "" 0 "" {TEXT -1 89 " 2. It works with differential equations for which no explicit solution c an be found." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "DEplot(\{diff(y(x), x) = x*sin(y(x))\}, \{y(x)\},\n x=-2..2, [[y(0)=1/4]], y=-1..1); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "4 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 }