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-1 8 1 {CSTYLE "" -1 -1 " Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 15 2 } {PSTYLE "R3 Font 2" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 261 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 262 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 263 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 257 0 "" }{TEXT 258 19 "Separab le Equations" }{TEXT 256 0 "" }}{PARA 258 "" 0 "" {TEXT 259 14 "Brian \+ E. Blank" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 83 "Click on a [+] sign to expand a section. Click on a [-] s ign to collapse a section." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 "I" }{TEXT 512 11 "ntroduction" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 388 7 "In this" }{TEXT -1 2 " " }{TEXT 260 5 "MAPLE" } {TEXT -1 4 " " }{HYPERLNK 17 "worksheet" 2 "worksheet" "" }{TEXT 387 14 ", we will use" }{TEXT -1 2 " " }{TEXT 261 5 "MAPLE" }{TEXT -1 3 " " }{TEXT 386 54 "to solve separable first order differential \+ equations." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 259 "" 0 "" {TEXT -1 9 "Key Words" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 152 "The words and symbols that are used in this worksheet have been collected here as hypertext links. C lick on any word to go to the correspond help page." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "Dchangevar" 2 "Dchang evar" "" }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "DEtools" 2 "D Etools" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "dfieldplot " 2 "dfieldplot" "" }{TEXT -1 3 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "diff" 2 "diff" "" }{TEXT 515 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "d isplay" 2 "display" "" }{TEXT -1 1 " " }{TEXT 516 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "dsolve" 2 "dsolve" "" }{TEXT -1 2 " " }}{PARA 15 " " 0 "" {HYPERLNK 17 "for" 2 "for" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 " " {HYPERLNK 17 "implicitplot" 2 "implicitplot" "" }{TEXT -1 1 " " }} {PARA 15 "" 0 "" {HYPERLNK 17 "int" 2 "int" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "LambertW" 2 "LambertW" "" }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "loop" 2 "loop" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 " " {HYPERLNK 17 "lists" 2 "lists" "" }{TEXT -1 2 " " }}{PARA 15 "" 0 " " {HYPERLNK 17 "normal" 2 "normal" "" }{TEXT -1 3 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "odeadvisor" 2 "odeadvisor" "" }{TEXT -1 1 " " }} {PARA 15 "" 0 "" {HYPERLNK 17 "odetest" 2 "odetest" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "op" 2 "op" "" }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "packages" 2 "packages" "" }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "plot" 2 "plot" "" }{TEXT 382 1 " " }{TEXT -1 0 "" } }{PARA 15 "" 0 "" {HYPERLNK 17 "plots" 2 "plots" "" }{TEXT -1 0 "" }} {PARA 15 "" 0 "" {HYPERLNK 17 "plot,structure" 2 "plot,structure" "" } {TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "restart" 2 "restart" " " }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "selection" 2 "select ion" "" }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "solve" 2 "solv e" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "subs" 2 "subs" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "value" 2 "value" " " }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "with\n" 2 "with" "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 385 34 "On-line information abo ut using a " }{TEXT 381 6 " MAPLE" }{TEXT -1 2 " " }{TEXT 383 59 "fun ction can also be obtained at a prompt by preceding the " }{TEXT 380 5 "exact" }{TEXT 384 52 " keyword by a question mark and executing tha t line." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 510 52 "Classification of First Order Differential Equations" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 347 89 "All of t he equations that appear in this worksheet are first order differentia l equations" }}{PARA 0 "" 0 "" {TEXT 354 11 "of the form" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT 348 24 "y '(x) = F( x , y(x) ) ." }} {PARA 261 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 355 73 "Someti mes this equation will be accompanied by an initial value condition" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " } {TEXT 349 3 "y(x" }{TEXT 350 1 "0" }{TEXT 351 5 ") = y" }{TEXT 352 1 " 0" }{TEXT 353 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT 356 77 "There are a number of \"types\" that such equations ma y fall into. There is a " }{TEXT 357 5 "MAPLE" }{TEXT -1 1 " " } {TEXT 360 10 " function," }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT 358 10 "odeadvisor" }{TEXT -1 1 "," }{TEXT 361 7 " in the" }{TEXT -1 2 " " }{TEXT 359 7 "DEtools" }{TEXT 362 63 " package that can classi fy first order differential equations." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 363 4 "If " }{TEXT 364 3 "ode" }{TEXT 365 17 " is the equation" }{TEXT -1 1 " " }{TEXT 366 22 "to be classified , then" }{TEXT -1 2 " " }{TEXT 367 16 "odeadvisor(ode) " }{TEXT 368 25 "is the appropriate call. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 369 8 "Example:" }}{PARA 0 "" 0 "" {TEXT -1 1 " \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "ode := diff(y(x),x) = x*y(x) ^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/-%%diffG6$-%\"yG6#%\"xG F,*&F,\"\"\")F)\"\"#F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "o deadvisor(ode);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%+_separableG" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 370 76 "To find a description of separable equations, execute the next help demand:\n " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "?odeadvisor,separable" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 518 81 "An eve n more direct approach combines the previous two steps into one: just \+ add " }{TEXT 519 4 "help" }{TEXT 520 19 " as an argument to" }{TEXT -1 2 " " }{TEXT 517 10 "odeadvisor" }{TEXT -1 2 ": " }{TEXT 521 109 " the type of equation is printed in the worksheet and the relevant info rmation page is automatically opened up" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "odeadvi sor(ode,help);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%+_separableG" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 527 55 "There is even an approach that minimizes the amount of " }{TEXT 528 5 "MAPLE" }{TEXT 529 132 " syntax that the user needs to know (and minimizes ty ping, to boot). Just enter the differential equation, position the mou se over " }{TEXT 530 5 "MAPLE" }{TEXT 531 239 "'s output, and right c lick. A menu will pop up, offering the choice of solving the different ial equation, of adding an initial condition, or of classifying the di fferential equation. There are other choices as well. A screen capture of a " }{TEXT 532 5 "MAPLE" }{TEXT 533 25 " session will illustrate. 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