{VERSION 4 0 "IBM INTEL LINUX22" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 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 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "h:=dsolve(\{diff(y(x ),x)=exp(y(x)*x),y(0)=1\},\{y(x)\},type=numeric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGR6#%(rkf45_xG6'%\"iG%(rkf45_sG%)outpointG%#r1G%#r 2G6#%aoCopyright~(c)~1993~by~the~University~of~Waterloo.~All~rights~re served.G6\"C&>8&-%&evalfG6#9$@$52-%$absG6#,$F3!\"\"-F<6#,&&%,loc_contr olG6#\"\"#\"\"\"F3F?4-%'memberG6$&FD6#\"\"'<*!\"#F?FGFF$F?\"\"!$FGFR$F PFR$FFFRC%>FD-%%copyG6#=F06#;FG\"#EE\\[l;FGFGFF$FRFR\"\"$Fjn\"\"%$FG! \")\"\"&F]oFNFG\"\"($FG!\"*\"\")\"&++$\"\"*\"%+5\"#5FR\"#6FR\"#7FR\"#8 FR\"#9FR\"#:FR\"#;FR\"#FR\"#?FS\"#@FR\"#AFR\"#BFR\"#CFR\" #DFRFhnFR>%'loc_y0G-FY6#=F06#;FGFGE\\[l\"FGFS>%'loc_y1G-FY6#=F0F\\qE\\ [l!@$0F;FRC$>&FD6#F[oF3@%1%'DigitsG-%'evalhfG6#F]rC$>8%-%*traperrorG6# -F_r6#-%=dsolve/numeric_solnall_rkf45G6,%&loc_FG-%$varG6#FD-F^s6#Fhp-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@$/Fcr%*lasterrorGC%>8'-%+searchtextG6$.F _r-%(convertG6$-%#opG6$FG7#Fcr%%nameG>8(-F]u6$.%)hardwareGF`u@%50F[uFR 0FiuFR-Fjr6,F\\sFDFhpF`qFfsFisF\\tF_tFbtFet-%&ERRORG6#FcrFbv7$/%\"xGF7 -%$seqG6$/&%$ordG6#,&8$FGFGFG&Fhp6#Fbw/FbwF]qF06%FDFhpF`qF0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(h(x),x=-1..1);" }} {PARA 8 "" 1 "" {TEXT -1 101 "Error, (in dsolve/numeric_solnall_rkf45) cannot evaluate boolean: abs(x)-max(.1e-7,.1e-7*abs(x)) < 0\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "odeplot(h,[x,y(x)],-3.. 1);" }}{PARA 7 "" 1 "" {TEXT -1 99 "Warning, rkf45 is unable to achiev e requested accuracy at 17 of 50 points,\nplot may be incomplete.\n" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "f:=y->simplify(diff(y(x),x)-y(x)^2);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"yG6\"6$%)operatorG%&arrowGF(-%)simpl ifyG6#,&-%%diffG6$-9$6#%\"xGF6\"\"\"*$)F3\"\"#F7!\"\"F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f(x->x^n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"xG,&%\"nG\"\"\"F)!\"\"F)F(F)F))F&,$F(\"\"#F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "DEplot3(\{diff(y(x),x)=2*sin (2*Pi*x)\},[y(x)],x=-1.1..1,[[y(1)=1],[y(.5)=-2]],stepsize=.01);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "dfieldplot(\{diff(y(x),x)=1/ y(x)^3\},[y(x)],x=-1..1,y(x)=-1..1,color=sin(.03/y(x)^3));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "dfield" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "fieldplot([-2*y,x],x=-1..1,y=-1..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "fp1:=fieldplot([x,y+x],x=-1..1,y=-1 ..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "dsolve(diff(y(x),x )=y(x)/x+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG*&,&-%#l nGF&\"\"\"%$_C1GF,F,F'F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "sp1:=plot(\{seq((ln(x)+c)*x,c=-5..5)\},x=-1..1,color=red):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "display(\{fp1,sp1\},view=[-1 ..1,-1..1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "fp2:=fieldplot([x," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 45 "Warni ng, the name adjoint has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been redefined an d unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "A:=matri x([[cos(.3), sin(.3)], [-sin(.3), cos(.3)]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7$$\"+\"*[O`&*!#5$\"+n??bHF,7$$!+n? ?bHF,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "B:=matrix([[0, - 1],[1, 0]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7$7$ \"\"!!\"\"7$\"\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "eva lm(C &* B &* inverse(C));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrix G6#7$7$#!\"(\"\"'#\"#<\"#77$#!\"&\"\"$#\"\"(F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "C:=matrix([[3, 5], [6, 2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7$7$\"\"$\"\"&7$\"\"'\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "fieldplot([(-14*x+17*y),(-20 *x+14*y)],x=-1..1,y=-1..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "dsolve(\{diff(y(x),x)=(-20*x+14*y(x))/(-14*x+17*y(x)),y(0)=.25\}); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6$/-%\"yG6#%\"xG,$*&,&*&F'\"\"\"-%%s qrtG6#\"# " 0 "" {MPLTEXT 1 0 75 "plot( 1/4*(56/289*x*sqrt(17) +1/17*sqrt(-2304/17*x^2+17))*sqrt(17),x=-1..1);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "fieldplot([x,-y^2+x*cos (x*y)],x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "36 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }