{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "_cstyle1" -1 204 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_ pstyle1" -1 200 1 {CSTYLE "" -1 -1 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle2" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 14 "with(DEtools):" } }}{EXCHG {PARA 201 "" 0 "" {TEXT -1 16 "3.1 Exercise 14:" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 120 "phaseportrait(diff(y(x),x)=x*y( x)+4*x,y(x),x=-1.5..1.5,[seq([y(0)=k], k=-9..5)],y=-10..10,arrows=none , linecolor=black);" }}}{EXCHG {PARA 200 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 204 11 "dfieldplot(" }{MPLTEXT 1 -1 41 "diff(y(x),x)=x*y(x)+4*x,y(x),x=-1.5..1.5," }{MPLTEXT 1 204 11 " y=-10..5);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 204 5 "diff( " }{MPLTEXT 1 -1 10 "x*y(x)+4*x" }{MPLTEXT 1 204 4 ",x);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 8 "y(x)+x*(" }{MPLTEXT 1 -1 10 "x*y( x)+4*x" }{MPLTEXT 1 -1 4 ")+4;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 204 10 "factor(%);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 37 "dsolve(diff(y(x),x)=x*y(x)+4*x,y(x));" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 32 "plot(-4+2*exp(1/2*x^2),x=-1..1);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 33 "plot(-4+10*exp(1/2*x^2),x=-1..1) ;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 33 "plot(-4+.1*exp(1/2* x^2),x=-1..1);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 32 "plot(- 4-2*exp(1/2*x^2),x=-1..1);" }}}{EXCHG {PARA 201 "" 0 "" {TEXT -1 17 "3 .1 Exercise #18:" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 123 "pha seportrait(diff(y(x),x)=x*y(x)-x*y(x)^3,y(x),x=-1.5..1.5,[seq([y(0)=k] , k=-5..5)],y=-5..5,arrows=none, linecolor=black);" }}}{EXCHG {PARA 200 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 204 11 "dfieldplot(" }{MPLTEXT 1 -1 13 "diff(y(x),x)=" }{MPLTEXT 1 -1 15 "x*y(x)-x*y(x)^3" }{MPLTEXT 1 -1 18 ",y(x),x=-1.5..1.5," }{MPLTEXT 1 204 10 " y=-1..1);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 204 11 "dfieldplot(" }{MPLTEXT 1 -1 46 "diff(y(x),x)=x*y(x)-x*y(x)^3,y(x),x=- 1.5..1.5," }{MPLTEXT 1 204 10 " y=-5..5);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 204 5 "diff(" }{MPLTEXT 1 -1 15 "x*y(x)-x*y(x)^3" } {MPLTEXT 1 204 4 ",x);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 8 "y(x)+x*(" }{MPLTEXT 1 -1 15 "x*y(x)-x*y(x)^3" }{MPLTEXT 1 -1 21 ")-y( x)^3-3*x*y(x)^2*(" }{MPLTEXT 1 -1 15 "x*y(x)-x*y(x)^3" }{MPLTEXT 1 -1 2 ");" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 204 10 "factor(%);" }} }{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 7 "dsolve(" }{MPLTEXT 1 -1 35 "diff(y(x),x)=x*y(x)-x*y(x)^3,y(x));" }}}{EXCHG {PARA 200 "> " 0 " " {MPLTEXT 1 -1 37 "plot(1/(1+2*exp(-x^2))^(1/2),x=0..5);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 -1 38 "plot(-1/(1+2*exp(-x^2))^(1/2),x= 0..5);" }}}{EXCHG {PARA 200 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }