{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 "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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "eq:=diff(y(x),x,x)-d iff(y(x),x)/x-3*y(x)/x^2-ln(x)-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#eqG,,-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F,\"\"#\"\"\"*&-F'6$F)F,F1F,!\" \"F5*(\"\"$F1F)F1F,!\"#F5-%#lnGF+F5F1F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "eqt:=diff(y(t),t,t)-2*diff(y(t),t)-3*y(t)-(1+t)*exp(2 *t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqtG,*-%%diffG6$-%\"yG6#%\" tG-%\"$G6$F,\"\"#\"\"\"*&F0F1-F'6$F)F,F1!\"\"*&\"\"$F1F)F1F5*&,&F1F1F, F1F1-%$expG6#,$*&F0F1F,F1F1F1F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "eval(eqt,y(t)=(A*t+B)*exp(2*t))/exp(2*t):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&\"\"#\"\"\"%\"AGF&F&*(\"\"$F&F'F&%\"tGF&!\"\"*&F)F&%\"BGF&F+ F&F+F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "A:=-1/3; B:=( 2*A-1)/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG#!\"\"\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG#!\"&\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "eval(eqt,y(t)=C1*exp(3*t)+C2*exp(-t)-(t/3+5/9 )*exp(2*t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 44 "eval(eq,y(x)=C1*x^3+C2/x-(ln(x)/3+5/9)*x^2):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Deal ing with 3 by 3 matrices:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "eq:=diff(y(x),x,x,x)+3*diff(y(x),x,x)+3*diff(y(x ),x)+y(x)-1/x+3/x^2-6/x^3+6/x^4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #eqG,2-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F,\"\"$\"\"\"*&F0F1-F'6$F)-F.6$F, \"\"#F1F1*&F0F1-F'6$F)F,F1F1F)F1*&F1F1F,!\"\"F<*&F0F1F,!\"#F1*&\"\"'F1 F,!\"$F<*&F@F1F,!\"%F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "w ith(linalg): ybasic:=[exp(-x),x*exp(-x),x^2*exp(-x)];" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have bee n redefined and unprotected\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'yb asicG7%-%$expG6#,$%\"xG!\"\"*&F*\"\"\"F&F-*&)F*\"\"#F-F&F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "M:=wronskian(ybasic,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7%7%-%$expG6#,$%\"xG!\"\"* &F.\"\"\"F*F1*&)F.\"\"#F1F*F17%,$F*F/,&F*F1F0F/,&*(F4F1F.F1F*F1F1F2F/7 %F*,&*&F4F1F*F1F/F0F1,(*&F4F1F*F1F1*(\"\"%F1F.F1F*F1F/F2F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A:=augment(M,[0,0,1/x-3/x^2+6/x^3-6 /x^4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7&-%$ex pG6#,$%\"xG!\"\"*&F.\"\"\"F*F1*&)F.\"\"#F1F*F1\"\"!7&,$F*F/,&F*F1F0F/, &*(F4F1F.F1F*F1F1F2F/F57&F*,&*&F4F1F*F1F/F0F1,(*&F4F1F*F1F1*(\"\"%F1F. F1F*F1F/F2F1,**&F1F1F.F/F1*&\"\"$F1F.!\"#F/*&\"\"'F1F.!\"$F1*&FHF1F.! \"%F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A:=addrow(A,1,2,-A [2,1]/A[1,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7% 7&-%$expG6#,$%\"xG!\"\"*&F.\"\"\"F*F1*&)F.\"\"#F1F*F1\"\"!7&F5F*,$*(F4 F1F.F1F*F1F1F57&F*,&*&F4F1F*F1F/F0F1,(*&F4F1F*F1F1*(\"\"%F1F.F1F*F1F/F 2F1,**&F1F1F.F/F1*&\"\"$F1F.!\"#F/*&\"\"'F1F.!\"$F1*&FFF1F.!\"%F/" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A:=addrow(A,1,3,-A[3,1]/A[1, 1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7&-%$expG6 #,$%\"xG!\"\"*&F.\"\"\"F*F1*&)F.\"\"#F1F*F1\"\"!7&F5F*,$*(F4F1F.F1F*F1 F1F57&F5,$*&F4F1F*F1F/,&*&F4F1F*F1F1*(\"\"%F1F.F1F*F1F/,**&F1F1F.F/F1* &\"\"$F1F.!\"#F/*&\"\"'F1F.!\"$F1*&FFF1F.!\"%F/" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 32 "A:=addrow(A,2,3,-A[3,2]/A[2,2]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7&-%$expG6#,$%\"xG!\"\"*&F. \"\"\"F*F1*&)F.\"\"#F1F*F1\"\"!7&F5F*,$*(F4F1F.F1F*F1F1F57&F5F5,$*&F4F 1F*F1F1,**&F1F1F.F/F1*&\"\"$F1F.!\"#F/*&\"\"'F1F.!\"$F1*&FBF1F.!\"%F/ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "wp:=A[3,4]/A[3,3];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#wpG,$*&#\"\"\"\"\"#F(*&,**&F(F(%\"x G!\"\"F(*&\"\"$F(F-!\"#F.*&\"\"'F(F-!\"$F(*&F3F(F-!\"%F.F(-%$expG6#,$F -F.F.F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "vp:=-A[2,3]*wp /A[2,2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vpG,$*(%\"xG\"\"\"-%$ex pG6#,$F'!\"\"F-,**&F(F(F'F-F(*&\"\"$F(F'!\"#F-*&\"\"'F(F'!\"$F(*&F4F(F '!\"%F-F(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "up:=(-A[1,2] *vp-A[1,3]*wp)/A[1,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#upG,$*&# \"\"\"\"\"#F(*(%\"xGF),**&F(F(F+!\"\"F(*&\"\"$F(F+!\"#F.*&\"\"'F(F+!\" $F(*&F3F(F+!\"%F.F(-%$expG6#,$F+F.F.F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "evalm( ybasic&* [int(up,x),int(vp,x),int(wp,x)]);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&-%$expG6#,$%\"xG!\"\"\"\"\",(*&#F +\"\"#F+*&F)F+F%F*F+F+*&F/F+F%F*F**(\"\"$F+F)F*F%F*F+F+F+*(F)F+F%F+,(* &F+F+F%F*F**(F3F+F)F*F%F*F+*(F3F+F)!\"#F%F*F*F+F+*()F)F/F+F%F+,(*&F.F+ *&F+F+*&F)F+F%F+F*F+F+*&F+F+*&F;F+F%F+F*F**&F+F+*&)F)F3F+F%F+F*F+F+F+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$%\"xG!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "sol:=evalm(ybasic &* [C1,C2,C3]+1/x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG,**&-%$expG6#,$%\"xG!\"\"\"\"\" %#C1GF-F-*(F+F-F'F-%#C2GF-F-*()F+\"\"#F-F'F-%#C3GF-F-*&F-F-F+F,F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eval(eq,y(x)=sol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Euclid algorithm:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "a:=2^3*3^4*5^4*7^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"aG\")+]%)>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "b:=2^2* 3^6*5^2*7^4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"*+H.v\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "c:=a mod b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\")+]%)>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "d:=b mod c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG \")+HF;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "e:=c mod d;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG\"(+@d$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f:=d mod e;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"fG\"(+X)>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "g:=e mod f; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG\"(+we\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "h:=f mod g;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG\"'+pR" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "g mod \+ h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "gcd(a,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"'+pR " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "2^2*3^4*5^2*7^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"'+pR" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "p0:=x^8-28*x^7+337*x^6-2274*x^5+9396*x^4-24312*x^3+38 432*x^2-33920*x+12800;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p0G,4*$)% \"xG\"\")\"\"\"F**&\"#GF*)F(\"\"(F*!\"\"*&\"$P$F*)F(\"\"'F*F**&\"%uAF* )F(\"\"&F*F/*&\"%'R*F*)F(\"\"%F*F**&\"&7V#F*)F(\"\"$F*F/*&\"&K%QF*)F( \"\"#F*F**&\"&?R$F*F(F*F/\"&+G\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "p1:=gcd(p0,diff(p0,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p1G,.\"$?$!\"\"*&\"$W&\"\"\"%\"xGF*F**&\"$c$F*)F+\"\"#F*F'*& \"$7\"F*)F+\"\"$F*F**&\"# " 0 "" {MPLTEXT 1 0 23 "p2:=gcd(p1,diff(p1,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p2G,(*$)%\"xG\"\"#\"\"\"F**&\"\"'F*F(F*! \"\"\"\")F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "p3:=gcd(p2,d iff(p2,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p3G\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "quo(p1,p2^2,x,'r');" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"\"\"\"&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "r;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "solve(p2,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"%\"\"#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "solve(p1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\" \"&\"\"#F$\"\"%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "solve( p0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*\"\"&F#\"\"#F$F$\"\"%F%F%" } }}}{MARK "45" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }