{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 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 "Heading 1" -1 3 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart;\nwith(plots ):\nwith(DEtools):" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 51 "Example 1: A differential equation and slope field\n" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "DE1:=diff(y(x), x) = y(x)-2*x;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "DEplot(DE1, \+ y(x), x=-3..3, y=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "initialCondition:=[[0,1]];\nDEplot(DE1, y(x), x=-3..3, initialConditi on,y=-3..3,linecolor=blue);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "So lve for the " }{TEXT 261 16 "general solution" }{TEXT -1 29 " to the d ifferential equation" }{MPLTEXT 1 0 19 "\ndsolve(DE1, y(x));" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Use the initial condition to get t he particular solution to the " }{TEXT 260 21 "initial value problem" }{TEXT -1 0 "" }{MPLTEXT 1 0 54 "\nsubs(\{y(x)=1,x=0\},y(x)=2+2*x+exp( x)*C1);\nsolve(%,C1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "y: =x->2+2*x+exp(x)*(-1);\nplot(y(x),x=-3..3,y=-3..3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Several particular solutions at once on the sam e slope field." }{MPLTEXT 1 0 124 "\ny:='y':\nmoreInitConds:=[[0,2],[0 ,1],[0,-1]];\nDEplot(DE1, y(x), x=-3..3, moreInitConds,y=-3..3,linecol or=[red,blue,maroon]);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 57 "Example 2: Differential Equa tion for an Electric Circuit\n" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 " A differential equation for an electric circuit" }{MPLTEXT 1 0 37 "\ny :='y':\nDE2:=diff(y(x),x)=15-3*y(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "A particular solution plotted on the slope field" }{MPLTEXT 1 0 96 "\ninitialCondition:=[[0,0]];\nDEplot(DE2, y(x), x=-1..7,initialC ondition,y=-1..7,linecolor=blue);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Several particular solutions plotted simultaneously" }{MPLTEXT 1 0 114 "\nmoreInitConds:=[[0,0],[0,5],[0,7]];\nDEplot(DE2, y(x), x=-1 ..7,moreInitConds,y=-1..7,linecolor=[blue,red,maroon]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 16 "General solution" }{TEXT -1 46 " to the \+ electric circuit differential equation" }{MPLTEXT 1 0 19 "\ndsolve(DE2 , y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "subs(\{y(x)=0,x =0\},y(x)=5+exp(-3*x)*C1);\nsolve(%,C1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 19 "Particular solution" }{TEXT -1 28 " for initial conditio n (0,0)" }{MPLTEXT 1 0 52 "\ny:=x->5+exp(-3*x)*(-5);\nplot(y(x),x=-1.. 7,y=-1..7);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 59 "Ex ample 3: Differential Equation for a Brine Mixing Problem" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "y:='y ':\nDE3:=diff(y(x),x)=.75-y(x)/200;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "initialCondition:=[[0,20]];\nDEplot(DE3, y(x), x=-5. .1000,initialCondition,y=-5..200,linecolor=blue);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Several particular solutions plotted simultaneo usly" }{MPLTEXT 1 0 124 "\nmoreInitConds:=[[0,20],[0,150],[0,180]];\nD Eplot(DE3, y(x), x=-5..1000,moreInitConds,y=-5..200,linecolor=[blue,re d,maroon]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 264 16 "General solution" }{TEXT -1 46 " to the electric \+ circuit differential equation" }{MPLTEXT 1 0 19 "\ndsolve(DE3, y(x)); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "subs(\{y(x)=0,x=0\},y(x )=150+exp(-1/200*x)*C1);\nsolve(%,C1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 19 "Particular solution" }{TEXT -1 28 " for initial conditio n (0,0)" }{MPLTEXT 1 0 65 "\ny:=x->150+exp(-1/200*x)*(-150);\nplot(y(x ),x=-5..1000,y=-5..200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 0 0" 9 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }