{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 1 10 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "New century schoolbook" 0 12 0 0 0 0 2 2 2 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 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 -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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Lucidatypewriter" 0 12 0 0 0 0 2 2 2 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 0 12 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 11 " HIGHLIGHTS" }}{PARA 0 "" 0 "" {TEXT -1 16 "Denise Kirschner" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(DEtools):with(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "diffeq:=diff(y(x),x,x)+2* diff(y(x),x)-3*y(x)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'diffeqG/, (-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"\"-F(6$F*F-F1F*!\"$\"\"!" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Char_eq:=r^2+2*r-3; " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(Char_eqG,(*$)%\"rG\"\"#\"\"\"\"\"\" F(F)!\"$F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ev:=solve(%,r );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#evG6$!\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y(x)=C1*exp(ev[1]*x)+C2*exp(ev[2]*x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,&*&%#C1G\"\"\"-%$ expG6#,$F'!\"$F+F+*&%#C2GF+-F-F&F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "subs(%,diffeq):expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " plot(1*exp(ev[1]*x)+2*exp(ev[2]*x), x=0..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7U7$\"\"!$\"\"$F(7$$ \"1LLL3x&)*3\"!#;$\"1yE>!\\29&H!#:7$$\"1nm\"H2P\"Q?F.$\"1-Y'o%yq%*HF17 $$\"1LL$eRwX5$F.$\"1*p?.#36AJF17$$\"1ML$3x%3yTF.$\"1PDghYyALF17$$\"1nm \"z%4\\Y_F.$\"1)Rp26dpe$F17$$\"1MLeR-/PiF.$\"150#y+0c)QF17$$\"1***\\il 'pisF.$\"1%4h'4[)yC%F17$$\"1MLe*)>VB$)F.$\"1;!QGnE(zYF17$$\"1++DJbw!Q* F.$\"1'Ge'3_2q^F17$$\"1nm;/j$o/\"F1$\"1SQh1,^SdF17$$\"1LL3_>jU6F1$\"13 ?PxDZ-jF17$$\"1++]i^Z]7F1$\"1FKv3z[2qF17$$\"1++](=h(e8F1$\"1C)4Ep4(*z( F17$$\"1++]P[6j9F1$\"1,'oiY%>^')F17$$\"1L$e*[z(yb\"F1$\"1%Hb`D0o]*F17$ $\"1nm;a/cq;F1$\"1j[HT^pj5!#97$$\"1nmm;t,mF1$\"1R1;Fgp7$$\"1+](=xpe=#F1$\"1];8y)=)zFgp7$$\"1n;zpSS\"R#F1$\"1\"=[9@Ue=#Fgp7$$\"1LL3_?`(\\#F 1$\"1YrWt([0V#Fgp7$$\"1M$e*)>pxg#F1$\"1hU02'*y8FFgp7$$\"1+]Pf4t.FF1$\" 1wjSM-5()HFgp7$$\"1MLe*Gst!GF1$\"1(ook)yG8LFgp7$$\"1+++DRW9HF1$\"1TlR= ss(o$Fgp7$$\"1++DJE>>IF1$\"1$)R'p^i\\4%Fgp7$$\"1+]i!RU07$F1$\"1ipzF=uJ XFgp7$$\"1++v=S2LKF1$\"1l\\&zY.:2&Fgp7$$\"1mmm\"p)=MLF1$\"1#*z`vp76cFg p7$$\"1++](=]@W$F1$\"1[`s**3#3D'Fgp7$$\"1L$e*[$z*RNF1$\"1u(*\\ERC$*oFg p7$$\"1,+]iC$pk$F1$\"1=v]_mOrwFgp7$$\"1m;H2qcZPF1$\"1ag`j@b$[)Fgp7$$\" 1+]7.\"fF&QF1$\"1W*)f]6eC%*Fgp7$$\"1mm;/OgbRF1$\"1E\"e+DWX/\"!#87$$\"1 +]ilAFjSF1$\"1d!4Qj'Gj6Ffw7$$\"1MLL$)*pp;%F1$\"1Y5%pB$R!H\"Ffw7$$\"1ML 3xe,tUF1$\"1xJ^gKvM9Ffw7$$\"1n;HdO=yVF1$\"1*>1c0jQf\"Ffw7$$\"1,++D>#[Z %F1$\"1@'\\.Pzbv\"Ffw7$$\"1nmT&G!e&e%F1$\"15V#*z9?h>Ffw7$$\"1MLL$)Qk%o %F1$\"1q8_pTVl@Ffw7$$\"1+]iSjE!z%F1$\"1$*Q=(GomS#Ffw7$$\"1+++DM\"3%[F1 $\"1>o?V`WJDFfw7$$\"1,]P40O\"*[F1$\"17-,R;piEFfw7$$\"1,voa-oX\\F1$\"1= c*)*yG8\"GFfw7$$\"\"&F($\"1b06&=j#oHFfw-%'COLOURG6&%$RGBG$\"#5!\"\"F(F (-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(F_[l%(DEFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "diffeq:=diff(y(x),x$2)+4*diff(y(x),x)+3*y(x)=0;inits: =y(0)=2,D(y)(0)=-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'diffeqG/,(-% %diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"\"-F(6$F*F-\"\"%F*\"\"$\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&initsG6$/-%\"yG6#\"\"!\"\"#/--%\" DG6#F(F)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "### WARNI NG: `dsolve` has been extensively rewritten, many new result forms can occur and options are slightly different, see help page for details\n sol:=dsolve(\{diffeq,inits\},y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$solG/-%\"yG6#%\"xG,&-%$expG6#,$F)!\"$#!\"\"\"\"#-F,6#,$F)F1#\"\"&F 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "subs(%,diffeq):expand( %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!F$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "plot(rhs(sol), x=0..10);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7X7$\"\"!$\"\"#F(7$$ \"1LLL3x&)*3\"!#;$\"17g\"3o+8)=!#:7$$\"1nmm;arz@F.$\"1[66OxO]K^y+m7F17$$\"1nmmm6m #G(F.$\"1yWj8Ih]6F17$$\"1ommT&phN)F.$\"1^HbC\\DV5F17$$\"1,+v=ddC%*F.$ \"15RnX\\)eW*F.7$$\"1LLe*=)H\\5F1$\"1r^46M()R&)F.7$$\"1nm\"z/3uC\"F1$ \"1U\"RM_-F1(F.7$$\"1++DJ$RDX\"F1$\"1;E4\"\\S`y&F.7$$\"1nm\"zR'ok;F1$ \"1^>*=Zftp%F.7$$\"1++D1J:w=F1$\"1mR8F. 7$$\"1nm\"z*ev:JF1$\"1+CCQ$)=36F.7$$\"1MLL347TLF1$\"1X$e1-(4Z))!#<7$$ \"1MLLLY.KNF1$\"1q]Tns35tF`r7$$\"1++D\"o7Tv$F1$\"1/qn![jY&eF`r7$$\"1LL L$Q*o]RF1$\"1<6TH>+5[F`r7$$\"1,+D\"=lj;%F1$\"1ne4@c%p(QF`r7$$\"1++vV&R Y2aF1$\"17#=$)\\Y27\"F`r7$$\"1nm;zXu9c F1$\"16UYxkK4\"*!#=7$$\"1+++]y))GeF1$\"1mH-FKN`tFhu7$$\"1++]i_QQgF1$\" 1N'yZC7N'fFhu7$$\"1,+D\"y%3TiF1$\"1&[VG1]$p[Fhu7$$\"1++]P![hY'F1$\"1em d?,,))QFhu7$$\"1LLL$Qx$omF1$\"1!z$HT`9wJFhu7$$\"1+++v.I%)oF1$\"1#*z?(z H$fDFhu7$$\"1mm\"zpe*zqF1$\"1@N$>\\>X5#Fhu7$$\"1,++D\\'QH(F1$\"1]E3K)R #*p\"Fhu7$$\"1LLe9S8&\\(F1$\"1$=*4([b%*Q\"Fhu7$$\"1,+D1#=bq(F1$\"1['*[ J\"Qe7\"Fhu7$$\"1LLL3s?6zF1$\"1'>,(oJHl\"*!#>7$$\"1++DJXaE\")F1$\"1R5H (o&p*Q(F`y7$$\"1ommm*RRL)F1$\"1[YCVDf0gF`y7$$\"1om;a<.Y&)F1$\"1S_&HYmy &[F`y7$$\"1NLe9tOc()F1$\"1M(fh\"*)QORF`y7$$\"1,++]Qk\\*)F1$\"1%pzJM%eW KF`y7$$\"1NL$3dg6<*F1$\"1X^KDO*)*f#F`y7$$\"1ommmxGp$*F1$\"1:NhxIgK@F`y 7$$\"1++D\"oK0e*F1$\"1UBLqP]E " 0 "" {MPLTEXT 1 0 73 "diffeq2:=diff(y(x),x$2)-2*dif f(y(x),x)+6*y(x)=0;inits2:=y(0)=1,D(y)(0)=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(diffeq2G/,(-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\" \"\"-F(6$F*F-!\"#F*\"\"'\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'in its2G6$/-%\"yG6#\"\"!\"\"\"/--%\"DG6#F(F)\"\"$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 186 "### WARNING: `dsolve` has been extensively re written, many new result forms can occur and options are slightly diff erent, see help page for details\nsol2:=dsolve(\{diffeq2, inits2\}, y( x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol2G/-%\"yG6#%\"xG,&*&-%$e xpGF(\"\"\"-%$cosG6#*&-%%sqrtG6#\"\"&\"\"\"F)F.F.F.*(F3F7F,F7-%$sinGF1 F.#\"\"#F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(rhs(sol2 ), x=0..10);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6% -%'CURVESG6$7go7$\"\"!$\"\"\"F(7$$\"1nmm;arz@!#;$\"1'\\zM6_'>;!#:7$$\" 1LL$e9ui2%F.$\"1;'HwS'f$)>F17$$\"1nmm\"z_\"4iF.$\"1i$QIXsS(>F17$$\"1om mT&phN)F.$\"1z?+(4dbH\"F17$$\"1LLe*=)H\\5F1$!1RS&3bhKv\"F.7$$\"1nm\"z/ 3uC\"F1$!1(y>jLXI>#F17$$\"1++DJ$RDX\"F1$!1'>%fLIqbYF17$$\"1nm\"zR'ok;F 1$!1#pqT!et5qF17$$\"1++D1J:w=F1$!1&QG+F\"H.$)F17$$\"1MLL3En$4#F1$!1?I= rFQ/vF17$$\"1nm;/RE&G#F1$!12)H\\![;*H%F17$$\"1+++D.&4]#F1$\"1?y\"fg-xW #F17$$\"1+++vB_(*4?R0HFho7$$\"1++D\"o7Tv$F1$\"1S`+q#pw2\"Fho7$$\"1 LLL$Q*o]RF1$!1pgg[n4FY2aF1$\"13_'3Vn92\"Ffr7$$\"1nm;zXu9cF1$\"1EuQ-;A;F Ffr7$$\"1+++]y))GeF1$\"1PeBe,H0WFfr7$$\"1++]i_QQgF1$\"1e6b*e(G0bFfr7$$ \"1,+D\"y%3TiF1$\"1$Rqz!H=WaFfr7$$\"1++]P![hY'F1$\"1j7IPi0CMFfr7$$\"1L LL$Qx$omF1$!1j9,x&e.l%Fho7$$\"1+++v.I%)oF1$!1)eFnNv(*e'Ffr7$$\"1mm\"zp e*zqF1$!1.'*y(f\"e48!#77$$\"1,++D\\'QH(F1$!1;'\\Q52x&>Fcv7$$\"1n;zp%* \\%R(F1$!18zt&p?E<#Fcv7$$\"1LLe9S8&\\(F1$!1r`px#[**G#Fcv7$$\"1****\\i+ tZvF1$!1Q0P6(zCI#Fcv7$$\"1nmT5hK+wF1$!1j#o1vdhF#Fcv7$$\"1MLLe@#Hl(F1$! 15*Q]oKr?#Fcv7$$\"1,+D1#=bq(F1$!1Y6McT(=4#Fcv7$$\"1n;H2FO3yF1$!1_TlS8_ @^')F1$\"1PdfY9.guFcv7$$\"1NLe9tOc()F1$\"1[Skhsv?&)Fcv7$$\"1, vV[ko/))F1$\"1D%)o&z1**)))Fcv7$$\"1p;H#e0I&))F1$\"1\"p[L%Q\"f;*Fcv7$$ \"1^(=#\\^;x))F1$\"1,i1kLwk#*Fcv7$$\"1Ne9;ZK,*)F1$\"1O!\\_Jt_L*Fcv7$$ \"1>H2$G%[D*)F1$\"1*HZ'3yyv$*Fcv7$$\"1,++]Qk\\*)F1$\"13*zbdwYQ*Fcv7$$ \"1oT5SMLx*)F1$\"1)*))[D3\"RN*Fcv7$$\"1N$3-.B]+*F1$\"13H'exlrF*Fcv7$$ \"1-DJ?ErK!*F1$\"156`th=_\"*Fcv7$$\"1pmT5ASg!*F1$\"1kFR7k\"o(*)Fcv7$$ \"1.]i!R\"y:\"*F1$\"1]DNzx(oY)Fcv7$$\"1NL$3dg6<*F1$\"1=Omi$4Ft(Fcv7$$ \"1,+voTAq#*F1$\"1G$z,ZnU#eFcv7$$\"1ommmxGp$*F1$\"1DyMIVB?JFcv7$$\"1,D J&**)4A%*F1$\"1&G6^l6>N\"Fcv7$$\"1M$eRA5\\Z*F1$!1$oTt]QBP'Ffr7$$\"1nTg _9sF&*F1$!1/]4%GJ_Fcv7$$\"1+]il(z5j* F1$!1&eW,t\")po(Fcv7$$\"1,++]oi\"o*F1$!1l!\\`C2!G5!#67$$\"1-]PMR " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 35 "Warning, new definition for adjoint" }} {PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }} {PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Wronskian([exp(-2*x),x*exp(- 2*x)],x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$-%$expG6 #,$%\"xG!\"#*&F,\"\"\"F(F/7$,$F(F-,&F(F/F.F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)-%$ expG6#,$%\"xG!\"#\"\"#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "R EDUCTION OF ORDER IS NEXT, we need one solution!\n" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 54 "diffeq:=x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)= 0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'diffeqG/,(*&)%\"xG\"\"#\"\" \"-%%diffG6$-%\"yG6#F)-%\"$G6$F)F*\"\"\"F5*&F)F5-F-6$F/F)F5F*F/!\"#\" \"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sol1:=y(x)=x;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol1G/-%\"yG6#%\"xGF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(sol1,diffeq); expand(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&)%\"xG\"\"#\"\"\"-%%diffG6$F'-%\" $G6$F'F(\"\"\"F0*&F'F0-F+6$F'F'F0F(F'!\"#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " subs(y(x)=v(x)*rhs(sol1),diffeq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ ,(*&)%\"xG\"\"#\"\"\"-%%diffG6$*&-%\"vG6#F'\"\"\"F'F1-%\"$G6$F'F(F1F1* &F'F)-F+6$F-F'F1F(F-!\"#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&)%\"xG\"\"$\" \"\"-%%diffG6$-%\"vG6#F'-%\"$G6$F'\"\"#\"\"\"F4*&)F'F3F)-F+6$F-F'F4\" \"%\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "reduced:=subs(d iff(v(x),x)=z(x),%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(reducedG/,& *&)%\"xG\"\"$\"\"\"-%%diffG6$-%\"zG6#F)F)\"\"\"F2*&)F)\"\"#F+F/F2\"\"% \"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "REMEBER! THIS IS ALWAYS \+ SEPERABLE!!" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "### WARNING: `dsolv e` has been extensively rewritten, many new result forms can occur and options are slightly different, see help page for details\ndsolve(red uced,z(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"zG6#%\"xG*&%$_C1G \"\"\"*$)F'\"\"%F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " v(x)=int(rhs(%),x)+C2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"vG6#%\" xG,&*&%$_C1G\"\"\"*$)F'\"\"$F+!\"\"#!\"\"\"\"$%#C2G\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "IT MAY BE HELPFUL TO USE THE SIMPLIFY COM MAND HERE such as simplify(int(rhs(....etc..))" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "rhs(sol1)*rhs(%); sol2:=y(x)=expand(%);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",&*&%$_C1G\"\"\"*$)F$\"\"$F)!\"\"#! \"\"\"\"$%#C2GF%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol2G/-%\"yG6 #%\"xG,&*&%$_C1G\"\"\"*$)F)\"\"#F-!\"\"#!\"\"\"\"$*&F)\"\"\"%#C2GF6F6 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(sol2,diffeq): expa nd(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "WHAT IS THE LONGTERM BEHAVIOR OF y????" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "_C1:=1; C2:=2;sol2;plot(rhs(sol2), x=1..1 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$_C1G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#C2G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\" yG6#%\"xG,&*&\"\"\"F**$)F'\"\"#F*!\"\"#!\"\"\"\"$F'\"\"#" }}{PARA 13 " " 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"\"\" \"!$\"1nmmmmmm;!#:7$$\"1++](Quh>\"F-$\"1o^suUQf@F-7$$\"1+]7tY'oO\"F-$ \"1URz[eJbDF-7$$\"1++D^P#)e:F-$\"1&z*eB%p/)HF-7$$\"1++ve_0_F-$\"1/l*pdm0!QF-7$$\"1+]7VsmA@F-$\"1P:/(Qa8<%F- 7$$\"1+]7)R&G2BF-$\"1K'HU7c>b%F-7$$\"1+]7ex@)\\#F-$\"1@Q?fg-V\\F-7$$\" 1+]i&zP&)o#F-$\"1zu.T,'4L&F-7$$\"1++]Z`I%)GF-$\"1&G^K#GaGdF-7$$\"1++v8 vtcIF-$\"1`.?`,!y2'F-7$$\"1++]#Hb3D$F-$\"1.A=.!p,Z'F-7$$\"1++]P,xXMF-$ \"1b[!e:mM'oF-7$$\"1++]2ngLOF-$\"1&[$[9o'>C(F-7$$\"1+]73.=/QF-$\"1?o@C5!#97$$\"1+]iDt_/`F-$\"1,H$z#3sf5Ffr7$$\"1***\\Ppd b\\&F-$\"1q)y\"Gy+)4\"Ffr7$$\"1+]7eX)Rp&F-$\"1\"*)>gyox8\"Ffr7$$\"1+]( os:n'eF-$\"1`t$)pYPs6Ffr7$$\"1++D@,F`gF-$\"1oUKBVu47Ffr7$$\"1*****\\1* *fC'F-$\"1?Z4'QX$[7Ffr7$$\"1++DOnaMkF-$\"10yAgU5'G\"Ffr7$$\"1+]7.j(ph' F-$\"1[%RS&RjA8Ffr7$$\"1++vLK`>oF-$\"1!)G(Q*)*=j8Ffr7$$\"1*****\\kR:+( F-$\"1%=Vg&zi*R\"Ffr7$$\"1,+]P.(e>(F-$\"1h89D.`Q9Ffr7$$\"1+]7GG'>P(F-$ \"1k8$)4#zPZ\"Ffr7$$\"1,+]K%yWc(F-$\"1Ja=`JJ7:Ffr7$$\"1**\\781iXxF-$\" 1zJU<&o&[:Ffr7$$\"1+]i&Qm\\$zF-$\"1Hj[rQY'e\"Ffr7$$\"1++](['3?\")F-$\" 1._Fb<^B;Ffr7$$\"1**\\7y+*QJ)F-$\"1,&)*yw&Hi;Ffr7$$\"1,++qfa+&)F-$\"1g tC#*yk*p\"Ffr7$$\"1***\\(y&G9p)F-$\"15r'QXWyt\"Ffr7$$\"1,]7$eI2)))F-$ \"1%)e:mMsv/&=Ffr7$$\"1,++!**eBV*F-$\"1IDLPr4')=Ffr7$$\"1**\\78%zCi*F-$ \"1)))[2)e8C>Ffr7$$\"1+](o\"*[W!)*F-$\"1-/o?Iag>Ffr7$$\"#5F*$\"1nmmmmm **>Ffr-%'COLOURG6&%$RGBG$Ffz!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEW G6$;F(Fez%(DEFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "29 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }