Revisão Maple - Yuri Ki - 2012.2-09-12

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

2012.2-09-03.mws
{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 "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 }
{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 }{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 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 267 "" 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 "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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 
0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal
" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }
3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 
0 1 }{PSTYLE "Normal" -1 258 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 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 257 259 
1 {CSTYLE "" -1 -1 "" 1 14 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 "" 257 260 1 {CSTYLE "" -1 -1 "" 1 14 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 }}
{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT -1 6 "2012.2" }}{PARA 259 "" 0 
"" {TEXT -1 59 "Comportamento geom\351trico das solu\347\365es de equa
\347\365es lineares " }}{PARA 260 "" 0 "" {TEXT -1 49 "homog\352neas d
e ordem 2 com coeficientes constantes" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 79 "J\341 vimos que para resolver uma edo
 de segunda ordem com coeficientes constantes" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "a*diff(y(t),`$`(t,2))
+b*diff(y(t),t)+c*y(t) = 0;" "6#/,(*&%\"aG\"\"\"-%%diffG6$-%\"yG6#%\"t
G-%\"$G6$F.\"\"#F'F'*&%\"bGF'-F)6$-F,6#F.F.F'F'*&%\"cGF'-F,6#F.F'F'\"
\"!" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 23 "\351 importante analisar a" }{TEXT 257 23 " equa\347\343o
 caracter\355stica" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "
" {XPPEDIT 18 0 "a*lambda^2+b*lambda+c = 0.;" "6#/,(*&%\"aG\"\"\"*$%'l
ambdaG\"\"#F'F'*&%\"bGF'F)F'F'%\"cGF'-%&FloatG6$\"\"!F1" }}{PARA 0 "" 
0 "" {TEXT -1 83 "Note que no caso de equa\347\365es de ordem 2, a equ
a\347\343o caracter\355stica \351 de grau 2. Se " }{XPPEDIT 18 0 "lam
bda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 3 " e " }
{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" }
}{PARA 0 "" 0 "" {TEXT -1 70 "s\343o as ra\355zes de equa\347\343o car
acter\355stica, ent\343o temos 3 possibilidades:" }}{PARA 0 "" 0 "" 
{TEXT -1 3 "1) " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{XPPEDIT 18 
0 "_1;" "6#%#_1G" }{TEXT -1 3 " e " }{XPPEDIT 18 0 "lambda;" "6#%'lamb
daG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" }{TEXT -1 20 " reais e diferentes;
" }}{PARA 0 "" 0 "" {TEXT -1 3 "2) " }{XPPEDIT 18 0 "lambda;" "6#%'lam
bdaG" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 3 " = " }{XPPEDIT 18 0 
"lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" }{TEXT -1 7 " r
eais;" }}{PARA 0 "" 0 "" {TEXT -1 3 "3) " }{XPPEDIT 18 0 "lambda;" "6#
%'lambdaG" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 3 " e " }{XPPEDIT 
18 0 "lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" }{TEXT -1 
11 " complexos." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 258 8 "CASO 1) " }{TEXT -1 1 " " }{XPPEDIT 18 0 "lambda;" "6#%'l
ambdaG" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 3 " e " }{XPPEDIT 18 
0 "lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" }{TEXT -1 19 
" reais e diferentes" }}{PARA 0 "" 0 "" {TEXT -1 40 "A solu\347\343o \+
\351 da forma y (t) = C1 * exp( " }{XPPEDIT 18 0 "lambda;" "6#%'lambd
aG" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 19 " * t ) + C2 * exp( " 
}{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" 
}{TEXT -1 8 " * t ). " }}{PARA 0 "" 0 "" {TEXT -1 39 "Quando t aumenta
, a solu\347\343o (em m\363dulo)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 54 "a1) tende a zero (se os dois expoentes s
\343o negativos);" }}{PARA 0 "" 0 "" {TEXT -1 51 "b1) cresce r\341pido
 (se um dos expoentes \351 positivo);" }}{PARA 0 "" 0 "" {TEXT -1 76 "
c1) tende a uma constante (se um dos expoentes \351 nulo e o outro \+
\351 negativo)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 259 11 "EXEMPLO a1)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "with(plots): with(DEtools):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "edoa1:=diff(y(t),t,t)+5*diff
(y(t),t)+6*y(t)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&edoa1G/,(-%%d
iffG6$-%\"yG6#%\"tG-%\"$G6$F-\"\"#\"\"\"*&\"\"&F2-F(6$F*F-F2F2*&\"\"'F
2F*F2F2\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 
"" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dsolve(
edoa1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&%$_C1G\"
\"\"-%$expG6#,$*&\"\"$F+F'F+!\"\"F+F+*&%$_C2GF+-F-6#,$*&\"\"#F+F'F+F2F
+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "dsolve(\{edoa1,y(0)=
2,D(y)(0)=3\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&
\"\"(\"\"\"-%$expG6#,$*&\"\"$F+F'F+!\"\"F+F2*&\"\"*F+-F-6#,$*&\"\"#F+F
'F+F2F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solucaoa1:=rhs
(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*solucaoa1G,&*&\"\"(\"\"\"-%
$expG6#,$*&\"\"$F(%\"tGF(!\"\"F(F0*&\"\"*F(-F*6#,$*&\"\"#F(F/F(F0F(F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(solucaoa1, t=-2..3
, y=-20..5);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "
" {GLPLOT2D 235 222 222 {PLOTDATA 2 "6%-%'CURVESG6$7fn7$$!\"#\"\"!$!3w
Z3:/#=EL#!#97$$!3em;HdNvs>!#<$!35T'z'f(Gq8#F-7$$!3OLLe9r]X>F1$!3[wH@IS
Xd>F-7$$!3:+](=ng#=>F1$!3O2$Hh(=g#z\"F-7$$!3smm;HU,\"*=F1$!3****eySMGT
;F-7$$!3M$3_]C2t'=F1$!3S(pz8Cz(>:F-7$$!3&**\\P4E+O%=F1$!3A8*)HR_-29F-7
$$!3d;H#oF$*)>=F1$!3yFjS%z,CI\"F-7$$!3SL$3FH'='z\"F1$!3o2b/#oK`?\"F-7$
$!37+DcEV'Gu\"F1$!3%QJ%e8`*=,\"F-7$$!3gmmTgBa*o\"F1$!3CdCz%)\\'f[)!#:7
$$!3YmmmTp'ej\"F1$!3Y)\\l0vw)*4(F[o7$$!3amm\"H_\">#e\"F1$!3(*4#f&y/cKf
F[o7$$!30+D197xG:F1$!3O\"y*GCAZa\\F[o7$$!3ML$3_!4Nv9F1$!3h)*\\Cl2JJTF[
o7$$!3km;/wfHw8F1$!3E=B)\\SEh$HF[o7$$!3;+]PM.tt7F1$!3kyL()fFQY?F[o7$$!
3em;/,oln6F1$!3ONNwIX.&R\"F[o7$$!3%)**\\(oWB>1\"F1$!38)*)[[W:KS*!#;7$$
!3eJLLepjJ&*!#=$!3MSFd8/NhhFdq7$$!3Ulm;z/ot&)Fhq$!3#z,%>#o`c;%Fdq7$$!3
u)****\\P[_\\(Fhq$!3t&pNnulAg#Fdq7$$!3A*****\\7)Q7kFhq$!3)Hhr0+Vua\"Fd
q7$$!3e*****\\i^)o`Fhq$!3\"y*\\%*)\\6^q)F17$$!3vlmT50A@WFhq$!3-4gxG\"=
4e%F17$$!3OKLLeaR%H$Fhq$!3%3T,O\"*pLT\"F17$$!3kJLLLo#)RBFhq$\"3AtI#pdH
#pCFhq7$$!3f***\\PfO%H7Fhq$\"3c\"[\"Hsq\\'Q\"F17$$!3MSLLL3`lC!#>$\"3lg
#z'e(Gv\">F17$$\"3+L+]i!f#=$)Fft$\"3UB[(*y7cm@F17$$\"3+-+v=xpe=Fhq$\"3
sy3Fm.x(>#F17$$\"3<rm;H28IHFhq$\"3\"zT[m,RD5#F17$$\"3`nm\"zpSS\"RFhq$
\"3)y['**=%[1&>F17$$\"3)GLL3_?`(\\Fhq$\"3a322=&zPv\"F17$$\"3!fL$e*)>px
gFhq$\"3n5HUSx^Q:F17$$\"3w++v$f4t.(Fhq$\"3%>t7t^>_N\"F17$$\"3OPL$e*Gst
!)Fhq$\"3ochiJ#Q$p6F17$$\"3Y+++]#RW9*Fhq$\"3a+g)eT'R[**Fhq7$$\"3:++DJE
>>5F1$\"3B=(\\d&yRJ%)Fhq7$$\"3F+]i!RU07\"F1$\"3X.7qDDOVrFhq7$$\"3+++v=
S2L7F1$\"3$>.4-tB+\"fFhq7$$\"3Jmmm\"p)=M8F1$\"3u095#y7S'\\Fhq7$$\"3B++
](=]@W\"F1$\"3?\"eI5]Va5%Fhq7$$\"35L$e*[$z*R:F1$\"3y:Uq'[lnW$Fhq7$$\"3
e++]iC$pk\"F1$\"3fm$p!f-\\RGFhq7$$\"3[m;H2qcZ<F1$\"3%[5#3NT+hBFhq7$$\"
3O+]7.\"fF&=F1$\"3SGc8wO*H%>Fhq7$$\"3Ymm;/Ogb>F1$\"3#z())\\2nB.;Fhq7$$
\"3w**\\ilAFj?F1$\"3*[K>EBb*38Fhq7$$\"3yLLL$)*pp;#F1$\"35-M9kUFv5Fhq7$
$\"3)RL$3xe,tAF1$\"3)G3#omgO$y)Fft7$$\"3Cn;HdO=yBF1$\"3KF/J-a9zrFft7$$
\"3a+++D>#[Z#F1$\"3+V8#*3L!)ffFft7$$\"3SnmT&G!e&e#F1$\"3'G[D#fOo5[Fft7
$$\"3#RLLL)Qk%o#F1$\"3=c$*oMx?pRFft7$$\"37+]iSjE!z#F1$\"3pi\")y$\\H9B$
Fft7$$\"3a+]P40O\"*GF1$\"3)G*HD6#=El#Fft7$$\"\"$F*$\"3,Z!Rh4!\\W@Fft-%
'COLOURG6&%$RGBG$\"*++++\"!\")$F*F*Fa^l-%+AXESLABELSG6$%\"tG%\"yG-%%VI
EWG6$;F(Ff]l;$!#?F*$\"\"&F*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 
260 11 "EXEMPLO b1)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "edob
1:= 4*diff(y(t),t,t)-8*diff(y(t),t)+3*y(t)=0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&edob1G/,(*&\"\"%\"\"\"-%%diffG6$-%\"yG6#%\"tG-%\"$G6
$F0\"\"#F)F)*&\"\")F)-F+6$F-F0F)!\"\"*&\"\"$F)F-F)F)\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dsolve(edob1); " }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&%$_C1G\"\"\"-%$expG6#,$*&\"\"#!\"\"
F'F+F+F+F+*&%$_C2GF+-F-6#,$*(\"\"$F+F1F2F'F+F+F+F+" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 35 "dsolve(\{edob1,y(0)=2,D(y)(0)=1/2\});" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&#\"\"&\"\"#\"\"\"-%$
expG6#,$*&F,!\"\"F'F-F-F-F-*&#F-F,F--F/6#,$*(\"\"$F-F,F3F'F-F-F-F3" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "solucaob1:=rhs(%); \+
\ngraficob1:=plot(solucaob1, t=-6..5, y=-50..5):" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%*solucaob1G,&*&#\"\"&\"\"#\"\"\"-%$expG6#,$*&F)!\"\"%
\"tGF*F*F*F**&#F*F)F*-F,6#,$*(\"\"$F*F)F0F1F*F*F*F0" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 19 "display(graficob1);" }}{PARA 13 "" 1 "" 
{GLPLOT2D 223 194 194 {PLOTDATA 2 "6%-%'CURVESG6$7fn7$$!\"'\"\"!$\"3El
h<g'fSC\"!#=7$$!31nm;/8Bgd!#<$\"3^1s(*\\EK-9F-7$$!3YL$eR%)4;b&F1$\"3#f
'ewyPFc:F-7$$!3smm\"H>$*pJ&F1$\"3A<Na)f<'\\<F-7$$!3gmmT]8#33&F1$\"3ohN
\"*f2So>F-7$$!3EL$e9*>xX[F1$\"3NY\"Rhw[J@#F-7$$!3em;HZ6&yi%F1$\"3a<ki'
>wpY#F-7$$!3`+]iNn?-WF1$\"3gFr.m[CgFF-7$$!3ym;Hi\\%)oTF1$\"3/+>B\"[_)*
4$F-7$$!35+]7$eJi$RF1$\"3!e-Nj$*e$zMF-7$$!3GLL$38gpp$F1$\"3@e&GrL#Q<RF
-7$$!3ammT0(4i[$F1$\"3)Q.n(Q5iZVF-7$$!3y****\\UY&*[KF1$\"3GV;z7-8()[F-
7$$!3S++](QD2,$F1$\"3))z![L3hP\\&F-7$$!33++]dt9\"y#F1$\"3OY\"RX'H=YhF-
7$$!3/n;H7&oEd#F1$\"3:+vWxvf,oF-7$$!3VLL$3+nZK#F1$\"3#)4vZjtblwF-7$$!3
eLLL.>w9@F1$\"3qx\"4)p6au%)F-7$$!3A+]i]gZq=F1$\"3g@G8\")G**4&*F-7$$!3C
MLLy;Ca;F1$\"3_*)[px<X^5F17$$!3)***\\i+$)*pT\"F1$\"3a]?E.)p7<\"F17$$!3
k**\\(=]'3\">\"F1$\"3[=!3zh&R%H\"F17$$!3WJL$eR7Pb*F-$\"3g/64BODJ9F17$$
!3aILek/6*Q(F-$\"3%*['>$[usi:F17$$!37sm;a[Ha]F-$\"3f]X&)efX2<F17$$!3Yt
m\"Hix!HEF-$\"3iTt+oT*\\&=F17$$!35,+]P*)=z^!#>$\"3)pCj?fkM(>F17$$\"3=M
L$3P!>i<F-$\"3#)zHuf7**y?F17$$\"3Z*)****\\jw<TF-$\"3W^3LVPCW@F17$$\"3
\"3***\\()yBAkF-$\"3[(*Hp&=Qk8#F17$$\"3e$**\\PfK>l)F-$\"3*H\\cE'z`A?F1
7$$\"3Z***\\7%Gw76F1$\"3FcX_V012<F17$$\"3*emm;7:_L\"F1$\"3wrb`Ev%*o6F1
7$$\"3Y****\\7/ts:F1$\"3y_'R#)=k\"y>F-7$$\"3%GL3xcazy\"F1$!3SInoMIc%>
\"F17$$\"3$4++vT^K-#F1$!3W5#)=*fSS_$F17$$\"3il;/;ukWAF1$!3C!e2@vJ`\"oF
17$$\"3++](o-qgZ#F1$!3_v\"yET&)))=\"!#;7$$\"3vlm;HzK-FF1$!3R$34v9KW\">
Fcw7$$\"3g)*\\P%)*)>RHF1$!3VY/-7.m@IFcw7$$\"3;MLLjRLnJF1$!39VUF;R!oc%F
cw7$$\"38LLeH\\j+MF1$!3W%=,%*R))*RoFcw7$$\"3rm;/YS+KOF1$!3P2(4R!=z25!#
:7$$\"3\"3++]B3Y%QF1$!3(G&)GaVIoU\"F]y7$$\"3wL$e9VUk'RF1$!3%R>t_kokt\"
F]y7$$\"3omm\"ziw#)3%F1$!3^aQ'H`s'4@F]y7$$\"3%)**\\i&eYs>%F1$!3vDQJ?Ow
2DF]y7$$\"3/LLLVl@1VF1$!3a$yT#*)*ey(HF]y7$$\"3?mTNY7SAWF1$!39*y^F_5Hd$
F]y7$$\"3P**\\P\\feQXF1$!3GOa&p_KHG%F]y7$$\"3q*\\(=Ux=%f%F1$!3ma_deanp
YF]y7$$\"3/+++N&*y\\YF1$!33))**4JyX!4&F]y7$$\"3O+D\"yK\"R0ZF1$!3#>1dOn
^#[bF]y7$$\"3o+]i?J*4w%F1$!3ggUGRyGYgF]y7$$\"32](o/%[u?[F1$!3*>8b.Yu.j
'F]y7$$\"3M+DJgl\\!)[F1$!3q;b[3!\\(psF]y7$$\"3h]i:!G[-%\\F1$!3Mv1%yU6'
pzF]y7$$\"\"&F*$!3PHFEB(\\ct)F]y-%'COLOURG6&%$RGBG$\"*++++\"!\")$F*F*F
`^l-%+AXESLABELSG6$%\"tG%\"yG-%%VIEWG6$;F(Fe]l;$!#]F*Fe]l" 1 2 0 1 10 
0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 261 11 "EXEMPLO c1)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 40 "edoc1:= diff(y(t),t,t)+2*diff(y(t),t)=0;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%&edoc1G/,&-%%diffG6$-%\"yG6#%\"tG-%\"$G6$F
-\"\"#\"\"\"*&F1F2-F(6$F*F-F2F2\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "ci:=y(0)=1, D(y)(0)=2;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#ciG6$/-%\"yG6#\"\"!\"\"\"/--%\"DG6#F(F)\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dsolve(\{edoc1, ci\});" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&\"\"#\"\"\"-%$expG6#,$*&F)F*F'F
*!\"\"F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solucaoc1:=rhs(
%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*solucaoc1G,&\"\"#\"\"\"-%$ex
pG6#,$*&F&F'%\"tGF'!\"\"F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
87 "plot(solucaoc1, t=-5..10, y=-20..5);\nDEplot( edoc1, y(t), t=-5..1
0, y=-20..5, [[ci]] );" }}{PARA 13 "" 1 "" {GLPLOT2D 221 223 223 
{PLOTDATA 2 "6%-%'CURVESG6$7in7$$!\"&\"\"!$!3zr1[zlW-A!#87$$!33+v$fLI
\"f\\!#<$!3-CQVibcH?F-7$$!3:+](=ng#=\\F1$!3UNN]1ODq=F-7$$!3C+D\"y+\"Rx
[F1$!3$[K;^qXMs\"F-7$$!3J++vV8_O[F1$!3O#)eyT/;)e\"F-7$$!3Q+voz;l&z%F1$
!3'R)fIHM\\j9F-7$$!3[+]i:?yaZF1$!3#Q6()QE6'[8F-7$$!3b+Dc^B\"Rr%F1$!3:t
*>Q&fuU7F-7$$!3u****\\(oUIn%F1$!3Cg7U&y*=X6F-7$$!3e\\i:N<#>g%F1$!3`vlq
v:CL**!#97$$!3K+D\"Gy+3`%F1$!3QIQr1=%fh)Ffn7$$!3;](o/$)z'fWF1$!3W9:ep4
ItuFfn7$$!3++]7y)e&)Q%F1$!3+-`4\"Gh@['Ffn7$$!3#**\\(ozHfGUF1$!3moYk8')
y1ZFfn7$$!3%)***\\73F'oSF1$!3&Q\"QFJb^<MFfn7$$!3$)*****\\#3g2RF1$!3gJ<
j)e')fZ#Ffn7$$!3%)***\\(oXdYPF1$!3'*G4P(4)p$z\"Ffn7$$!3-+]i:F0EMF1$!3%
*=iMlFqQ%*!#:7$$!3;+]7Gz))GJF1$!3*QDt9>l0?&F_q7$$!3/+]7.5>@GF1$!3M#[uc
jR8!GF_q7$$!3(***\\7./(H]#F1$!3W7&e5xuHZ\"F_q7$$!3'***\\iS.x&=#F1$!36Z
O>g1b;x!#;7$$!3#*****\\(3\"\\f=F1$!32j<Pa:CARFdr7$$!3%)***\\P9/@d\"F1$
!3T@$>T%*H,7#Fdr7$$!3%)****\\7Xd[7F1$!3*e#yzV6y95Fdr7$$!3J/++vV;P#*!#=
$!3R)G5!4S^VVF17$$!3s)****\\([b1hFgs$!3%)=r.k6j\"R\"F17$$!3[***\\7`hOE
$Fgs$\"3%3\">w0q\"=#z!#>7$$\"3)p+++DO\"o6Fdt$\"3G!**z%H>4B5F17$$\"3?'*
*****\\>0)HFgs$\"3w2l5of/\\9F17$$\"3e%**\\(=-p6jFgs$\"3DUyL%R3qr\"F17$
$\"3o&*****\\2Mg#*Fgs$\"3;(o#p(o(3V=F17$$\"35+](=xZ&\\7F1$\"3V)[,bsSy
\">F17$$\"3;+]i:$4wb\"F1$\"3UT/K%>Jc&>F17$$\"3-++v=#R!z=F1$\"3-A([aZrm
(>F17$$\"3q+]P4A@u@F1$\"390*ec$G2()>F17$$\"3I++Dchf#\\#F1$\"3ky3AP:;$*
>F17$$\"3))**\\(of2L#GF1$\"3]F'Rpbqk*>F17$$\"3M**\\7yG>6JF1$\"3Y=-)\\
\\:!)*>F17$$\"3w++voo6AMF1$\"3g?-c<W$*)*>F17$$\"3q*****\\xJLu$F1$\"3wv
B/!\\R%**>F17$$\"3W++v$*yddSF1$\"35'*3bE5q**>F17$$\"3#***\\(=<F;O%F1$
\"3S(*zLVs$)**>F17$$\"35***\\i0A#*p%F1$\"3IB\\7Zr\"***>F17$$\"3&*)****
\\2mD+&F1$\"33:EZK[&***>F17$$\"3#)****\\i0XE`F1$\"3Ejy\"yOw***>F17$$\"
3K**\\(o/Q*>cF1$\"35Z)[.'o)***>F17$$\"3v,+](Q(zSfF1$\"3#H/fM3$****>F17
$$\"3()**\\(=-,FC'F1$\"3;$HY&=i****>F17$$\"3k+]P4tFelF1$\"3gv'[$))z***
*>F17$$\"3#*)***\\73\"o'oF1$\"3)=ukY\"*)****>F17$$\"3=+](oz;)*=(F1$\"3
/.79J%*****>F17$$\"3\\+++]*44](F1$\"3%\\)Ql%p*****>F17$$\"3-,+DJw/>yF1
$\"31(\\#RQ)*****>F17$$\"3(3+v=(4bM\")F1$\"3;rd,9******>F17$$\"3g,++vd
YC%)F1$\"3'pO\\=&******>F17$$\"3K,+Dc3uc()F1$\"3]iiAv******>F17$$\"37*
*****\\;$R0*F1$\"3/\"GFj)******>F17$$\"3C,](=-*zq$*F1$\"3[n^u#*******>
F17$$\"3w+]7G:3u'*F1$\"3s;X/'*******>F17$$\"#5F*$\"3IY)Qz*******>F1-%'
COLOURG6&%$RGBG$\"*++++\"!\")$F*F*Fa_l-%+AXESLABELSG6$%\"tG%\"yG-%%VIE
WG6$;F(Ff^l;$!#?F*$\"\"&F*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" }}}{PARA 13 "" 1 "" {GLPLOT2D 227 227 227 
{PLOTDATA 2 "6%-%'CURVESG6&7S7$%*undefinedGF(F'F'F'F'F'F'F'F'F'F'7$$!+
++]i:!\"*$!3]FG%4a))f2#!#;7$$!++++]7F,$!3^&GW74\\#=5F/7$$!++++v$*!#5$!
3HH$Hh&y\"3_%!#<7$$!++++]iF8$!3waIg,EM!\\\"F;7$$!++++DJF8$\"3v\"[Ex;Uv
J\"!#=7$$\"\"!FI$\"\"\"FI7$$\"++++DJF8$\"3!)*e#H\\'QZY\"F;7$$\"++++]iF
8$\"3[n:d<`\\8<F;7$$\"++++v$*F8$\"3ufI)>7Xm%=F;7$$\"++++]7F,$\"3MgP]h]
\"z\">F;7$$\"+++]i:F,$\"3;(H)**3J1c>F;7$$\"++++v=F,$\"3!f$**=(G#[w>F;7
$$\"+++](=#F,$\"3S5!)4%)=T()>F;7$$\"+++++DF,$\"39l@5r?E$*>F;7$$\"+++]7
GF,$\"3;ofO]MR'*>F;7$$FNF,$\"3s5\"*Gd&p!)*>F;7$$\"+++]PMF,$\"3e=P^8n'*
)*>F;7$$\"++++]PF,$\"3qxMFGpW**>F;7$$\"+++]iSF,$\"3kzFIkRq**>F;7$$\"++
++vVF,$\"3OG[xZ:%)**>F;7$$\"+++](o%F,$\"3iWG#>>:***>F;7$$\"+++++]F,$\"
3MPq(*4Y&***>F;7$$\"+++]7`F,$\"3_@tA3d(***>F;7$$\"++++DcF,$\"3?/3)***p
)***>F;7$$\"+++]PfF,$\"3;'>kO/$****>F;7$$FSF,$\"3C`=5\"G'****>F;7$$\"+
++]ilF,$\"33Yj(>,)****>F;7$$\"++++voF,$\"3?t2zP*)****>F;7$$\"+++](=(F,
$\"3Kj%[[V*****>F;7$$\"+++++vF,$\"3Q'z#)))p*****>F;7$$\"+++]7yF,$\"3)G
SW6%)*****>F;7$$\"++++D\")F,$\"3k>bV<******>F;7$$\"+++]P%)F,$\"3#p+pf&
******>F;7$$\"++++]()F,$\"3_z=Rx******>F;7$$\"+++]i!*F,$\"3;&\\E#))***
***>F;7$$FXF,$\"3]CPx$*******>F;7$$\"+++](o*F,$\"3y3)>o*******>F;7$$\"
+++++5!\")$\"3#y[9$)*******>F;-%&COLORG6&%$RGBG$\"\"*!\"\"Fhw$\"\"#Fjw
-%&STYLEG6#%%LINEG-%*THICKNESSG6#\"\"$-%%VIEWG6$;$!\"&FI$\"#5FI;$!#?FI
$\"\"&FI-%+AXESLABELSG6$Q\"t6\"Q%y(t)Ffy" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 46.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 43 "curva:=plot(solucaoc1, t=-5..10, y=-20..5):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f:=t-> 2:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 17 "reta:= plot(f): " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 22 "display(curva, reta); " }}{PARA 13 "" 1 "" 
{GLPLOT2D 239 239 239 {PLOTDATA 2 "6&-%'CURVESG6$7in7$$!\"&\"\"!$!3zr1
[zlW-A!#87$$!33+v$fLI\"f\\!#<$!3-CQVibcH?F-7$$!3:+](=ng#=\\F1$!3UNN]1O
Dq=F-7$$!3C+D\"y+\"Rx[F1$!3$[K;^qXMs\"F-7$$!3J++vV8_O[F1$!3O#)eyT/;)e
\"F-7$$!3Q+voz;l&z%F1$!3'R)fIHM\\j9F-7$$!3[+]i:?yaZF1$!3#Q6()QE6'[8F-7
$$!3b+Dc^B\"Rr%F1$!3:t*>Q&fuU7F-7$$!3u****\\(oUIn%F1$!3Cg7U&y*=X6F-7$$
!3e\\i:N<#>g%F1$!3`vlqv:CL**!#97$$!3K+D\"Gy+3`%F1$!3QIQr1=%fh)Ffn7$$!3
;](o/$)z'fWF1$!3W9:ep4ItuFfn7$$!3++]7y)e&)Q%F1$!3+-`4\"Gh@['Ffn7$$!3#*
*\\(ozHfGUF1$!3moYk8')y1ZFfn7$$!3%)***\\73F'oSF1$!3&Q\"QFJb^<MFfn7$$!3
$)*****\\#3g2RF1$!3gJ<j)e')fZ#Ffn7$$!3%)***\\(oXdYPF1$!3'*G4P(4)p$z\"F
fn7$$!3-+]i:F0EMF1$!3%*=iMlFqQ%*!#:7$$!3;+]7Gz))GJF1$!3*QDt9>l0?&F_q7$
$!3/+]7.5>@GF1$!3M#[ucjR8!GF_q7$$!3(***\\7./(H]#F1$!3W7&e5xuHZ\"F_q7$$
!3'***\\iS.x&=#F1$!36ZO>g1b;x!#;7$$!3#*****\\(3\"\\f=F1$!32j<Pa:CARFdr
7$$!3%)***\\P9/@d\"F1$!3T@$>T%*H,7#Fdr7$$!3%)****\\7Xd[7F1$!3*e#yzV6y9
5Fdr7$$!3J/++vV;P#*!#=$!3R)G5!4S^VVF17$$!3s)****\\([b1hFgs$!3%)=r.k6j
\"R\"F17$$!3[***\\7`hOE$Fgs$\"3%3\">w0q\"=#z!#>7$$\"3)p+++DO\"o6Fdt$\"
3G!**z%H>4B5F17$$\"3?'******\\>0)HFgs$\"3w2l5of/\\9F17$$\"3e%**\\(=-p6
jFgs$\"3DUyL%R3qr\"F17$$\"3o&*****\\2Mg#*Fgs$\"3;(o#p(o(3V=F17$$\"35+]
(=xZ&\\7F1$\"3V)[,bsSy\">F17$$\"3;+]i:$4wb\"F1$\"3UT/K%>Jc&>F17$$\"3-+
+v=#R!z=F1$\"3-A([aZrm(>F17$$\"3q+]P4A@u@F1$\"390*ec$G2()>F17$$\"3I++D
chf#\\#F1$\"3ky3AP:;$*>F17$$\"3))**\\(of2L#GF1$\"3]F'Rpbqk*>F17$$\"3M*
*\\7yG>6JF1$\"3Y=-)\\\\:!)*>F17$$\"3w++voo6AMF1$\"3g?-c<W$*)*>F17$$\"3
q*****\\xJLu$F1$\"3wvB/!\\R%**>F17$$\"3W++v$*yddSF1$\"35'*3bE5q**>F17$
$\"3#***\\(=<F;O%F1$\"3S(*zLVs$)**>F17$$\"35***\\i0A#*p%F1$\"3IB\\7Zr
\"***>F17$$\"3&*)****\\2mD+&F1$\"33:EZK[&***>F17$$\"3#)****\\i0XE`F1$
\"3Ejy\"yOw***>F17$$\"3K**\\(o/Q*>cF1$\"35Z)[.'o)***>F17$$\"3v,+](Q(zS
fF1$\"3#H/fM3$****>F17$$\"3()**\\(=-,FC'F1$\"3;$HY&=i****>F17$$\"3k+]P
4tFelF1$\"3gv'[$))z****>F17$$\"3#*)***\\73\"o'oF1$\"3)=ukY\"*)****>F17
$$\"3=+](oz;)*=(F1$\"3/.79J%*****>F17$$\"3\\+++]*44](F1$\"3%\\)Ql%p***
**>F17$$\"3-,+DJw/>yF1$\"31(\\#RQ)*****>F17$$\"3(3+v=(4bM\")F1$\"3;rd,
9******>F17$$\"3g,++vdYC%)F1$\"3'pO\\=&******>F17$$\"3K,+Dc3uc()F1$\"3
]iiAv******>F17$$\"37******\\;$R0*F1$\"3/\"GFj)******>F17$$\"3C,](=-*z
q$*F1$\"3[n^u#*******>F17$$\"3w+]7G:3u'*F1$\"3s;X/'*******>F17$$\"#5F*
$\"3IY)Qz*******>F1-%'COLOURG6&%$RGBG$\"*++++\"!\")$F*F*Fa_l-F$6$7S7$$
!#5F*$\"\"#F*7$$!3!pmmm\"p0k&*F1Fh_l7$$!3uKL$3<XZ=*F1Fh_l7$$!3WmmmT%p
\"e()F1Fh_l7$$!3/nmm\"4m(G$)F1Fh_l7$$!3OLL$3i.9!zF1Fh_l7$$!3fmm;/R=0vF
1Fh_l7$$!3k++]P8#\\4(F1Fh_l7$$!3Kmm;/siqmF1Fh_l7$$!3Q****\\(y$pZiF1Fh_
l7$$!3jKLL$yaE\"eF1Fh_l7$$!3<mmm\">s%HaF1Fh_l7$$!3]******\\$*4)*\\F1Fh
_l7$$!3o******\\_&\\c%F1Fh_l7$$!3%)******\\1aZTF1Fh_l7$$!3Imm;/#)[oPF1
Fh_l7$$!3%HLLL=exJ$F1Fh_l7$$!3lKLLL2$f$HF1Fh_l7$$!3%)****\\PYx\"\\#F1F
h_l7$$!3gLLLL7i)4#F1Fh_l7$$!3o)***\\P'psm\"F1Fh_l7$$!3?****\\74_c7F1Fh
_l7$$!3M:LL$3x%z#)FgsFh_l7$$!3()HLL3s$QM%FgsFh_l7$$!3]^omm;zr)*!#?Fh_l
7$$\"3fVLLezw5VFgsFh_l7$$\"3-.++v$Q#\\\")FgsFh_l7$$\"3%\\LL$e\"*[H7F1F
h_l7$$\"3=++++dxd;F1Fh_l7$$\"3e+++D0xw?F1Fh_l7$$\"35,+]i&p@[#F1Fh_l7$$
\"3++++vgHKHF1Fh_l7$$\"3ElmmmZvOLF1Fh_l7$$\"3%4+++v+'oPF1Fh_l7$$\"3UKL
$eR<*fTF1Fh_l7$$\"3K-++])Hxe%F1Fh_l7$$\"3!fmm\"H!o-*\\F1Fh_l7$$\"3X,+]
7k.6aF1Fh_l7$$\"3#emmmT9C#eF1Fh_l7$$\"33****\\i!*3`iF1Fh_l7$$\"3;NLLL*
zym'F1Fh_l7$$\"3'eLL$3N1#4(F1Fh_l7$$\"3,pm;HYt7vF1Fh_l7$$\"37-+++xG**y
F1Fh_l7$$\"3gpmmT6KU$)F1Fh_l7$$\"3qNLLLbdQ()F1Fh_l7$$\"3[++]i`1h\"*F1F
h_l7$$\"3A-+]P?Wl&*F1Fh_l7$Ff^lFh_lFj^l-%+AXESLABELSG6%%\"tG%\"yG-%%FO
NTG6#%(DEFAULTG-%%VIEWG6$;Ff_lFf^l;$FbdlF*$\"\"&F*" 1 2 0 1 10 0 2 9 
1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
262 8 "CASO 2) " }{TEXT -1 1 " " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG
" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "lam
bda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" }{TEXT -1 7 " reais
 " }}{PARA 0 "" 0 "" {TEXT -1 40 "A solu\347\343o \351 da forma y (t)
 = C1 * exp( " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "
_1;" "6#%#_1G" }{TEXT -1 23 " * t ) + C2 * t * exp( " }{XPPEDIT 18 0 "
lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 8 " * \+
t ). " }}{PARA 0 "" 0 "" {TEXT -1 65 "Quando t aumenta, a solu\347\343
o (em m\363dulo) \351 semelhante a ao caso 1." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "a2) tende a zero (se os d
ois expoentes s\343o negativos);" }}{PARA 0 "" 0 "" {TEXT -1 51 "b2) c
resce r\341pido (se um dos expoentes \351 positivo);" }}{PARA 0 "" 0 "
" {TEXT -1 76 "c2) tende a uma constante (se um dos expoentes \351 nul
o e o outro \351 negativo)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT 263 11 "EXEMPLO a2)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 46 "edoa2:=diff(y(t),t,t)+4*diff(y(t),t)+4*y(t)=0;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&edoa2G/,(-%%diffG6$-%\"yG6#%\"tG-%
\"$G6$F-\"\"#\"\"\"*&\"\"%F2-F(6$F*F-F2F2*&F4F2F*F2F2\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dsolve(edoa2); " }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&%$_C1G\"\"\"-%$expG6#,$*&\"\"
#F+F'F+!\"\"F+F+*(%$_C2GF+F,F+F'F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "dsolve(\{edoa1,y(0)=1,D(y)(0)=3\});" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&\"\"'\"\"\"-%$expG6#,$*&\"\"#F+F'F
+!\"\"F+F+*&\"\"&F+-F-6#,$*&\"\"$F+F'F+F2F+F2" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "solucaoa2:=rhs(%);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%*solucaoa2G,&*&\"\"'\"\"\"-%$expG6#,$*&\"\"#F(%\"tGF(!\"\"F(F(
*&\"\"&F(-F*6#,$*&\"\"$F(F/F(F0F(F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "plot(solucaoa2, t=-2..3, y=-20..5);" }}{PARA 13 "" 1 
"" {GLPLOT2D 243 237 237 {PLOTDATA 2 "6%-%'CURVESG6$7fn7$$!\"#\"\"!$!3
35[En]b*o\"!#97$$!3em;HdNvs>!#<$!3e[3-]tg[:F-7$$!3OLLe9r]X>F1$!3=:[_HX
;>9F-7$$!3:+](=ng#=>F1$!3xlHWe,I+8F-7$$!3smm;HU,\"*=F1$!3y,O6[<;\">\"F
-7$$!3M$3_]C2t'=F1$!3xjqf#p,N5\"F-7$$!3&**\\P4E+O%=F1$!3,FdmF@8A5F-7$$
!3d;H#oF$*)>=F1$!3y))RJZe3m%*!#:7$$!3SL$3FH'='z\"F1$!33km)y#p<l()FR7$$
!37+DcEV'Gu\"F1$!3q$>p2)ftntFR7$$!3gmmTgBa*o\"F1$!3'H['4OJ;(='FR7$$!3Y
mmmTp'ej\"F1$!3/P;I1\"*H%=&FR7$$!3amm\"H_\">#e\"F1$!3<Xi%=x.!RVFR7$$!3
0+D197xG:F1$!3RePR#>)3IOFR7$$!3ML$3_!4Nv9F1$!3T^t*fSwG.$FR7$$!3km;/wfH
w8F1$!3?V#=o)pWk@FR7$$!3;+]PM.tt7F1$!3mX]-e.X;:FR7$$!3em;/,oln6F1$!3[J
hINitS5FR7$$!3%)**\\(oWB>1\"F1$!3K]<)RQ2]2(!#;7$$!3eJLLepjJ&*!#=$!3?:2
l-<K*o%Fdq7$$!3Ulm;z/ot&)Fhq$!30%o'R8ta8KFdq7$$!3u)****\\P[_\\(Fhq$!33
?)3>>^10#Fdq7$$!3A*****\\7)Q7kFhq$!338*R.^S)f7Fdq7$$!3e*****\\i^)o`Fhq
$!3?#e:.'[5suF17$$!3vlmT50A@WFhq$!3r%)zT:;s4VF17$$!3OKLLeaR%H$Fhq$!3NK
WC?x\"y$=F17$$!3kJLLLo#)RBFhq$!3S4ju@]Wz]Fhq7$$!3f***\\PfO%H7Fhq$\"3'f
Iw\\\"*pJU%Fhq7$$!3MSLLL3`lC!#>$\"3gONwW8H%>*Fhq7$$\"3+L+]i!f#=$)Fft$
\"3Yf1()*\\cY=\"F17$$\"3+-+v=xpe=Fhq$\"3!p#Q#[[@VF\"F17$$\"3<rm;H28IHF
hq$\"3wG@#[!))Hj7F17$$\"3`nm\"zpSS\"RFhq$\"3#zo%e#\\6u>\"F17$$\"3)GLL3
_?`(\\Fhq$\"3!=0E\"3pD%4\"F17$$\"3!fL$e*)>pxgFhq$\"3TDJ'[`#[=(*Fhq7$$
\"3w++v$f4t.(Fhq$\"3&*f0i8?:J')Fhq7$$\"3OPL$e*Gst!)Fhq$\"3y`F(pg4)*\\(
Fhq7$$\"3Y+++]#RW9*Fhq$\"3\"*49?2du<kFhq7$$\"3:++DJE>>5F1$\"3Om=,r0Eka
Fhq7$$\"3F+]i!RU07\"F1$\"3A)H4\\tXmk%Fhq7$$\"3+++v=S2L7F1$\"3#3X%eG*Rv
&QFhq7$$\"3Jmmm\"p)=M8F1$\"3-*G9')=Y%[KFhq7$$\"3B++](=]@W\"F1$\"3?Q3&4
W9Hp#Fhq7$$\"35L$e*[$z*R:F1$\"35qu\\p*)*\\E#Fhq7$$\"3e++]iC$pk\"F1$\"3
!ow\\Q&Q;p=Fhq7$$\"3[m;H2qcZ<F1$\"3'4!=\"**)GQc:Fhq7$$\"3O+]7.\"fF&=F1
$\"37O4)GuxCG\"Fhq7$$\"3Ymm;/Ogb>F1$\"3)R5vq$[Qf5Fhq7$$\"3w**\\ilAFj?F
1$\"3-s10S\"G!e')Fft7$$\"3yLLL$)*pp;#F1$\"3O*[)fNgU=rFft7$$\"3)RL$3xe,
tAF1$\"3I*>2l+_\">eFft7$$\"3Cn;HdO=yBF1$\"3#3^B5[F&fZFft7$$\"3a+++D>#[
Z#F1$\"3)4t`xb>L&RFft7$$\"3SnmT&G!e&e#F1$\"3'Q!\\5:3'G>$Fft7$$\"3#RLLL
)Qk%o#F1$\"3$p+Vo\\Vbj#Fft7$$\"37+]iSjE!z#F1$\"3uVCYY'ol9#Fft7$$\"3a+]
P40O\"*GF1$\"3Ck0[xMri<Fft7$$\"\"$F*$\"3Kvk&RSYbU\"Fft-%'COLOURG6&%$RG
BG$\"*++++\"!\")$F*F*Fa^l-%+AXESLABELSG6$%\"tG%\"yG-%%VIEWG6$;F(Ff]l;$
!#?F*$\"\"&F*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 
0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "edob2:=diff(y(t),t,t)-diff(y(t),t)+0.25*y(t)=0;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&edob2G/,(-%%diffG6$-%\"yG6#%\"tG-%
\"$G6$F-\"\"#\"\"\"-F(6$F*F-!\"\"*&$\"#D!\"#F2F*F2F2\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dsolve(edob2); " }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&%$_C1G\"\"\"-%$expG6#,$*&\"\"
#!\"\"F'F+F+F+F+*(%$_C2GF+F,F+F'F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "dsolve(\{edob2,y(0)=2,D(y)(0)=2\});" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&\"\"#\"\"\"-%$expG6#,$*&F*!\"\"F'F
+F+F+F+*&F,F+F'F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solu
caob2:=rhs(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*solucaob2G,&*&\"
\"#\"\"\"-%$expG6#,$*&F'!\"\"%\"tGF(F(F(F(*&F)F(F/F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot(solucaob2, t=-10..10, y=-2..10
);" }}{PARA 13 "" 1 "" {GLPLOT2D 235 232 232 {PLOTDATA 2 "6%-%'CURVESG
6$7Z7$$!#5\"\"!$!3gt$o#*fd.R&!#>7$$!3!pmmm\"p0k&*!#<$!3Sw7an@\"zL'F-7$
$!3uKL$3<XZ=*F1$!3-Q%38a$GxsF-7$$!3WmmmT%p\"e()F1$!3_'G*4N3gs%)F-7$$!3
/nmm\"4m(G$)F1$!3z@QRY)eW$)*F-7$$!3OLL$3i.9!zF1$!3rRI)>[+b8\"!#=7$$!3f
mm;/R=0vF1$!3G![PprV8H\"FH7$$!3k++]P8#\\4(F1$!3qm1,B)=sY\"FH7$$!3Kmm;/
siqmF1$!3EA>i!)H!Hm\"FH7$$!3Q****\\(y$pZiF1$!35>;w!pf%o=FH7$$!3jKLL$ya
E\"eF1$!3Om8%yW8Y3#FH7$$!3<mmm\">s%HaF1$!3/Qm?@(z5F#FH7$$!3]******\\$*
4)*\\F1$!3!3rl>mHLY#FH7$$!3o******\\_&\\c%F1$!3TurP<?0<EFH7$$!3%)*****
*\\1aZTF1$!3WUf&Q-$p*p#FH7$$!3Imm;/#)[oPF1$!31`&H%>%4ro#FH7$$!3%HLLL=e
xJ$F1$!3j=$G61#Q3DFH7$$!3lKLLL2$f$HF1$!3-UST_hKc@FH7$$!3%)****\\PYx\"
\\#F1$!3BYq.`Ww99FH7$$!3gLLLL7i)4#F1$!3G6]'>@4NX$F-7$$!3o)***\\P'psm\"
F1$\"3_CZE+VgX9FH7$$!3?****\\74_c7F1$\"3I%Q?Ku-m'RFH7$$!3M:LL$3x%z#)FH
$\"3c,m!*e$zuu(FH7$$!3()HLL3s$QM%FH$\"3_F&H?qp*f7F17$$!3]^omm;zr)*!#?$
\"3%ojydMH.)>F17$$\"3fVLLezw5VFH$\"3ZD;UjF#e,$F17$$\"3-.++v$Q#\\\")FH$
\"32et_%[D3B%F17$$\"3%\\LL$e\"*[H7F1$\"3u$Q6sQ?>(fF17$$\"3=++++dxd;F1$
\"3S$\\!eO:7z$)F17$$\"3e+++D0xw?F1$\"3gh#po!fa^6!#;7$$\"35,+]i&p@[#F1$
\"35Fs,Sca]:F\\u7$$\"3++++vgHKHF1$\"3=&y<aJCp8#F\\u7$$\"3ElmmmZvOLF1$
\"3\"y+6eLx.$GF\\u7$$\"3%4+++v+'oPF1$\"31zBP)oZnz$F\\u7$$\"3UKL$eR<*fT
F1$\"3I[$Hv3$[I\\F\\u7$$\"3K-++])Hxe%F1$\"3B0eT#[L0`'F\\u7$$\"3!fmm\"H
!o-*\\F1$\"3y#Q+[E_XZ)F\\u7$$\"3X,+]7k.6aF1$\"3OEHP;V%)36!#:7$$\"3#emm
mT9C#eF1$\"3g2G!*)QzwV\"Few7$$\"33****\\i!*3`iF1$\"3eI9:$*yH\")=Few7$$
\"3;NLLL*zym'F1$\"3*o%zE-?AJCFew7$$\"3'eLL$3N1#4(F1$\"3=eq/QLr_JFew7$$
\"3,pm;HYt7vF1$\"35flwD^vqSFew7$$\"37-+++xG**yF1$\"3QW%*\\d1SR^Few7$$
\"3(eLL3U/37)F1$\"3U3;\\pq#)peFew7$$\"3gpmmT6KU$)F1$\"3#)R0\"y=_3q'Few
7$$\"3l-+]P$[/a)F1$\"3o\\0?$=\"RSvFew7$$\"3qNLLLbdQ()F1$\"39j**>'p;@[)
Few7$$\"33om\"zW?)\\*)F1$\"3RPQ'z4)[7'*Few7$$\"3[++]i`1h\"*F1$\"3gm_ML
W%*)3\"!#97$$\"3M,+++PDj$*F1$\"3'3BJ#oDhE7Fb[l7$$\"3A-+]P?Wl&*F1$\"3Qg
h<\\xC\"Q\"Fb[l7$$\"3w+]7G:3u'*F1$\"3#4g7^#40s9Fb[l7$$\"35,+v=5s#y*F1$
\"3g4UdMwoo:Fb[l7$$\"3W,]P40O\"*)*F1$\"3'R)4T0i_r;Fb[l7$$\"#5F*$\"3K>4
B4z&4y\"Fb[l-%'COLOURG6&%$RGBG$\"*++++\"!\")$F*F*Fh]l-%+AXESLABELSG6$%
\"tG%\"yG-%%VIEWG6$;F(F]]l;$!\"#F*F]]l" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "edoc2
:=diff(y(t),t,t)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&edoc2G/-%%di
ffG6$-%\"yG6#%\"tG-%\"$G6$F,\"\"#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "dsolve(edoc2); " }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/-%\"yG6#%\"tG,&*&%$_C1G\"\"\"F'F+F+%$_C2GF+" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT 
264 8 "CASO 3) " }{TEXT -1 1 " " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG
" }{XPPEDIT 18 0 "_1;" "6#%#_1G" }{TEXT -1 16 " = a + b * i e " }
{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{XPPEDIT 18 0 "_2;" "6#%#_2G" }
{TEXT -1 26 " = a - b * i (complexos)" }}{PARA 0 "" 0 "" {TEXT -1 
93 "A solu\347\343o \351 da forma y (t) = C1 * exp( a * t ) cos( b * \+
t ) + C2 * exp( a * t ) sen( b * t )" }}{PARA 0 "" 0 "" {TEXT -1 42 "Q
uando t aumenta, a solu\347\343o s\343o oscila\347\365es" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "a3) que diminuem (
se a \351 negativo);" }}{PARA 0 "" 0 "" {TEXT -1 31 "b3) aumentam (se \+
a \351 positivo);" }}{PARA 0 "" 0 "" {TEXT -1 44 "c3) nem aumentam nem
 diminuem (se a \351 nulo)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT 265 11 "EXEMPLO a3)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "edoa3:=diff(y(t),t,t)+diff
(y(t),t)+y(t)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&edoa3G/,(-%%dif
fG6$-%\"yG6#%\"tG-%\"$G6$F-\"\"#\"\"\"-F(6$F*F-F2F*F2\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dsolve(edoa3); " }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*(%$_C1G\"\"\"-%$expG6#,$*&\"\"#!\"\"
F'F+F2F+-%$sinG6#,$*(F1F2\"\"$#F+F1F'F+F+F+F+*(%$_C2GF+F,F+-%$cosGF5F+
F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "dsolve(\{edoa3,y(
0)=0,D(y)(0)=2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,$
*&#\"\"%\"\"$\"\"\"*(F,#F-\"\"#-%$expG6#,$*&F0!\"\"F'F-F6F--%$sinG6#,$
*(F0F6F,F/F'F-F-F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "D
Eplot( edoa3, y(t), t=-10..20, y=-20..20, [[y(0)=0,D(y)(0)=2]] );" }}
{PARA 13 "" 1 "" {GLPLOT2D 239 220 220 {PLOTDATA 2 "6%-%'CURVESG6&7S7$
%*undefinedGF(F'F'F'F'F'F'F'7$$!+++++]!\"*$\"3/=5a!og.h#!#;7$$!++++vVF
,$\"3Rq:BqB?T7F/7$$!++++]PF,$\"3yqBee`K$f\"!#<7$$!++++DJF,$!35S)y*4E`X
YF:7$$!+++++DF,$!3!>F:#y9oymF:7$$!++++v=F,$!3)e_yF**y*))eF:7$$!++++]7F
,$!3S#[!)>:o.\"QF:7$$!++++]i!#5$!33x;CkcLE;F:7$$\"\"!FWFV7$$\"++++]iFR
$\"3I*)*3%ew90()!#=7$$\"++++]7F,$\"3?MY3j))o\"4\"F:7$$\"++++v=F,$\"3T/
5F2M/J!*Fgn7$$\"+++++DF,$\"3S!)[4Nk>#[&Fgn7$$\"++++DJF,$\"3W[08zY5T?Fg
n7$$\"++++]PF,$!3=^s2S=9ZP!#>7$$\"++++vVF,$!3E&>dR\"GWi:Fgn7$$\"+++++]
F,$!3EM@\"Q,Z)e<Fgn7$$\"++++DcF,$!3%>wV9n1%p8Fgn7$$FZF,$!3/3\\$*>r#*ex
Fap7$$\"++++voF,$!3&>gc4Ka.S#Fap7$$\"+++++vF,$\"3bm4hYO$G9\"Fap7$$\"++
++D\")F,$\"3uO&\\(H8,=FFap7$$\"++++]()F,$\"352lDK(ooz#Fap7$$\"++++v$*F
,$\"3_*[AkWHE0#Fap7$$\"+++++5!\")$\"3StNOe44x5Fap7$$\"+++]i5Fas$\"3Q8%
)oVyd?D!#?7$$\"++++D6Fas$!3T!f/ZZcUg#Fis7$$\"+++](=\"Fas$!3*[*e&)>93:Y
Fis7$$FjnFas$!3g@'>b?#o$R%Fis7$$\"+++]78Fas$!3yf/.'[7(RIFis7$$\"++++v8
Fas$!35m@7(p`-Y\"Fis7$$\"+++]P9Fas$!3hA70zVFU?!#@7$$\"+++++:Fas$\"3o*y
Uk$z$[D&Fgu7$$\"+++]i:Fas$\"3?IV3yL3$o(Fgu7$$\"++++D;Fas$\"3S!)[9SJHAo
Fgu7$$\"+++](o\"Fas$\"3f[m?W17VWFgu7$$\"++++]<Fas$\"3%4a=+6+.#>Fgu7$$
\"+++]7=Fas$\"3Ag-)\\\"eW**H!#B7$$F_oFas$!3deVbk0M,**!#A7$$\"+++]P>Fas
$!31NFG]\"3xD\"Fgu7$$\"+++++?Fas$!3aHDT\"=Os/\"Fgu-%&COLORG6&%$RGBG$\"
\"*!\"\"Fjx$\"\"#F\\y-%&STYLEG6#%%LINEG-%*THICKNESSG6#\"\"$-%%VIEWG6$;
$FRFW$\"#?FW;$FisFWF\\z-%+AXESLABELSG6$Q\"t6\"Q%y(t)Fdz" 1 2 0 1 10 0 
2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 62 "DEplot( edoa3, y(t), t=0..10, y=-5..5, [[
y(0)=0,D(y)(0)=2]] );" }}{PARA 13 "" 1 "" {GLPLOT2D 257 233 233 
{PLOTDATA 2 "6%-%'CURVESG6&7S7$$\"\"!F)F(7$$\"+LLL$3#!#5$\"3*))pr*RL9M
P!#=7$$\"+mmmmTF-$\"3P]3`*3a-i'F07$$\"+******\\iF-$\"3Gu,fdw90()F07$$
\"+KLLL$)F-$\"39!3tnD6e+\"!#<7$$\"+mmmT5!\"*$\"3!Gnj*[zRw5F@7$$\"+****
**\\7FD$\"3[.$GJ'))o\"4\"F@7$$\"+KLLe9FD$\"3QOTHDi[h5F@7$$\"+lmmm;FD$
\"3%oD9Q(pCb**F07$$\"+)****\\(=FD$\"3`w=8<M/J!*F07$$\"+JLL$3#FD$\"3TBz
wO.4GzF07$$\"+kmm\"H#FD$\"3pvC2_:1BnF07$$\"+(******\\#FD$\"3!y/VHX'>#[
&F07$$\"+ILL3FFD$\"3/u`C'=w1E%F07$$\"+jmm;HFD$\"3Hbu)*\\!\\D5$F07$$\"+
'****\\7$FD$\"3#e6=%)p/6/#F07$$\"+HLLLLFD$\"3mC!H#)p(f*4\"F07$$\"+immT
NFD$\"3(4ZW.$HFAH!#>7$$\"+&*****\\PFD$!35;4&ppTru$F]q7$$\"+GLLeRFD$!3y
,(eG\"y*f,*F]q7$$\"+hmmmTFD$!3/SrFP+?%H\"F07$$\"+%****\\P%FD$!3qRT!z!G
Wi:F07$$\"+FLL$e%FD$!3b_fbBMC><F07$$\"+gmm\"z%FD$!3#*yIf<)Q%z<F07$$\"+
$*******\\FD$!37&Q\"o:q%)e<F07$$\"+ELL3_FD$!3cO'z\\$\\Yt;F07$$\"+fmm;a
FD$!3PVr.^/\")Q:F07$$\"+#****\\i&FD$!3y+GWymSp8F07$$\"+DLLLeFD$!3c.+Q)
)>Sy6F07$$\"+emmTgFD$!3)44#Q6F:t(*F]q7$$\"+\"*****\\iFD$!3m1`\"e?F*exF
]q7$$\"+CLLekFD$!3)z)>udtg?eF]q7$$\"+dmmmmFD$!3Ac`'49(e>SF]q7$$\"+!***
*\\(oFD$!3f^Wz$Ra.S#F]q7$$\"+BLL$3(FD$!31sREh@M>**!#?7$$\"+cmm\"H(FD$
\"3W)pn')*4O.>Fcv7$$\"+*)*****\\(FD$\"3(p)eJ-O$G9\"F]q7$$\"+ALL3xFD$\"
3](z!))eher=F]q7$$\"+bmm;zFD$\"3Cf&\\[eA-R#F]q7$$\"+))***\\7)FD$\"3Zc_
$fJ6!=FF]q7$$\"+@LLL$)FD$\"3KiV')zv/yGF]q7$$\"+ammT&)FD$\"3YJ*[19Kc*GF
]q7$$\"+()****\\()FD$\"3e>#4:uooz#F]q7$$\"+?LLe*)FD$\"3i;LS#Q$\\2EF]q7
$$\"+`mmm\"*FD$\"3-og\"pVR>N#F]q7$$\"+')***\\P*FD$\"3m#*[an%HE0#F]q7$$
\"+>LL$e*FD$\"3LTpdgtZH<F]q7$$\"+_mm\"z*FD$\"35D@9rBe*R\"F]q7$$\"+&)**
******FD$\"3gMM.!o!4x5F]q-%&COLORG6&%$RGBG$\"\"*!\"\"F^[l$\"\"#F`[l-%&
STYLEG6#%%LINEG-%*THICKNESSG6#\"\"$-%%VIEWG6$;F($\"#5F);$!\"&F)$\"\"&F
)-%+AXESLABELSG6$Q\"t6\"Q%y(t)Fj\\l" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
1 "E" }{TEXT 266 10 "XEMPLO b3)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "edob3:=16*diff(y(t),t,t)-8*d
iff(y(t),t)+145*y(t)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&edob3G/,
(*&\"#;\"\"\"-%%diffG6$-%\"yG6#%\"tG-%\"$G6$F0\"\"#F)F)*&\"\")F)-F+6$F
-F0F)!\"\"*&\"$X\"F)F-F)F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "dsolve(edob3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%
\"tG,&*(%$_C1G\"\"\"-%$expG6#,$*&\"\"%!\"\"F'F+F+F+-%$sinG6#,$*&\"\"$F
+F'F+F+F+F+*(%$_C2GF+F,F+-%$cosGF5F+F+" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 34 "dsolve(\{edob3,y(0)=-2,D(y)(0)=1\});" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&#\"\"\"\"\"#F+*&-%$expG6#,
$*&\"\"%!\"\"F'F+F+F+-%$sinG6#,$*&\"\"$F+F'F+F+F+F+F+*(F,F+F.F+-%$cosG
F7F+F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "DEplot( edob3, y(
t), t=-5..10, y=-10..10, [[y(0)=-2,D(y)(0)=1]] );" }}{PARA 13 "" 1 "" 
{GLPLOT2D 247 233 233 {PLOTDATA 2 "6%-%'CURVESG6&7S7$$!+++++]!\"*$\"3G
09G%pS:U$!#=7$$!+++](o%F*$!3z?5.Rlz1?F-7$$!++++vVF*$!37j\"4/Ve%olF-7$$
!+++]iSF*$!3-'>y*[\"\\+1'F-7$$!++++]PF*$!3J3o&e#Q/Fw!#?7$$!+++]PMF*$\"
3=YV-qFI()pF-7$$!++++DJF*$\"3U['pNuK9.*F-7$$!+++]7GF*$\"3Mtyxc6L*Q$F-7
$$!+++++DF*$!3!y2;`5)=@iF-7$$!+++](=#F*$!3i>IU)zKC>\"!#<7$$!++++v=F*$!
3c5R&*y6I()zF-7$$!+++]i:F*$\"3NaB-i-!*=PF-7$$!++++]7F*$\"3KzYX6,v49Ffn
7$$!++++v$*!#5$\"3cs$[xE(Rp8Ffn7$$!++++]iFio$\"3h$f!*=<HP/\"F-7$$FJFio
$!3?IKOv>Tn9Ffn7$$\"\"!Fgp$!\"#Fgp7$$\"++++DJFio$!3p_Y&3ir*R%)F-7$$\"+
+++]iFio$\"3I'zO-!**4e7Ffn7$$\"++++v$*Fio$\"3?iM93S$of#Ffn7$$\"++++]7F
*$\"3'4g33lGD&=Ffn7$$\"+++]i:F*$!3=VDId8j^mF-7$$\"++++v=F*$!3^1E4CO4<I
Ffn7$$\"+++](=#F*$!3w,GP^`e$3$Ffn7$$\"+++++DF*$!3Q]S[91&**=%F-7$$\"+++
]7GF*$\"399hpIE&)oIFfn7$$F\\qF*$\"3ZZrbB_L<WFfn7$$\"+++]PMF*$\"3MF2R!
\\*Rl?Ffn7$$\"++++]PF*$!3D!p0lV:6_#Ffn7$$\"+++]iSF*$!3jP_+?/>TcFfn7$$
\"++++vVF*$!3eA3W.U/sUFfn7$$\"+++](o%F*$\"3HzGTO*4z7\"Ffn7$$\"+++++]F*
$\"3azQ*=E7!QkFfn7$$\"+++]7`F*$\"3u[El(zH1#pFfn7$$\"++++DcF*$\"3o8tti&
Q,L\"Ffn7$$\"+++]PfF*$!3mw0-]Bu)Q'Ffn7$$FaqF*$!3uf\"4J0D8t*Ffn7$$\"+++
]ilF*$!35y#=)=T$[)\\Ffn7$$\"++++voF*$\"3gqRz=Da(*\\Ffn7$$\"+++](=(F*$
\"3Q;R^hdOA7!#;7$%*undefinedGF]xF\\xF\\xF\\xF\\xF\\xF\\xF\\xF\\x-%&COL
ORG6&%$RGBG$\"\"*!\"\"Fbx$\"\"#Fdx-%&STYLEG6#%%LINEG-%*THICKNESSG6#\"
\"$-%%VIEWG6$;$!\"&Fgp$\"#5Fgp;$FioFgpFey-%+AXESLABELSG6$Q\"t6\"Q%y(t)
F]z" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1
" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "E" }{TEXT 267 10 "XEMPLO c3)
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "edoc3:=diff(y(t),t,t)+9*y(t)=0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&edoc3G/,&-%%diffG6$-%\"yG6#%\"tG-%\"$G6$F-\"\"#\"\"
\"*&\"\"*F2F*F2F2\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "d
solve(edoc3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,&*&%$
_C1G\"\"\"-%$sinG6#,$*&\"\"$F+F'F+F+F+F+*&%$_C2GF+-%$cosGF.F+F+" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "dsolve(\{edoc3,y(0)=0,D
(y)(0)=3\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG-%$sinG6
#,$*&\"\"$\"\"\"F'F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "D
Eplot( edoc3, y(t), t=-5..10, y=-5..5, [[y(0)=0,D(y)(0)=3]] );" }}
{PARA 13 "" 1 "" {GLPLOT2D 221 235 235 {PLOTDATA 2 "6%-%'CURVESG6&7S7$
$!+++++]!\"*$!3\"3Uraq\"*G]'!#=7$$!+++](o%F*$!3wKE,XT:s**F-7$$!++++vVF
*$!3wx,Wh3D+`F-7$$!+++]iSF*$\"3'G8lzV@()p$F-7$$!++++]PF*$\"3Q&)yMAM4y'
*F-7$$!+++]PMF*$\"3wlUK(fojv(F-7$$!++++DJF*$!3E6d`f&fd(\\!#>7$$!+++]7G
F*$!35Gq/dAIX$)F-7$$!+++++DF*$!3-\"HqiI3+Q*F-7$$!+++](=#F*$!3a.=!*o3(p
v#F-7$$!++++v=F*$\"3PI_@_m#o6'F-7$$!+++]i:F*$\"3!=dRHb3p***F-7$$!++++]
7F*$\"3a'y#*[O:cr&F-7$$!++++v$*!#5$!35-&\\j>Y=B$F-7$$!++++]iFho$!3BsV0
-)f3a*F-7$$FIFho$!3o\"3/$)z631)F-7$$\"\"!FfpFep7$$\"++++DJFho$\"3o\"3/
$)z631)F-7$$\"++++]iFho$\"3BsV0-)f3a*F-7$$\"++++v$*Fho$\"35-&\\j>Y=B$F
-7$$\"++++]7F*$!3a'y#*[O:cr&F-7$$\"+++]i:F*$!3!=dRHb3p***F-7$$\"++++v=
F*$!3PI_@_m#o6'F-7$$\"+++](=#F*$\"3a.=!*o3(pv#F-7$$\"+++++DF*$\"3-\"Hq
iI3+Q*F-7$$\"+++]7GF*$\"35Gq/dAIX$)F-7$$FipF*$\"3E6d`f&fd(\\FL7$$\"+++
]PMF*$!3wlUK(fojv(F-7$$\"++++]PF*$!3Q&)yMAM4y'*F-7$$\"+++]iSF*$!3'G8lz
V@()p$F-7$$\"++++vVF*$\"3wx,Wh3D+`F-7$$\"+++](o%F*$\"3wKE,XT:s**F-7$$
\"+++++]F*$\"3[$4Aqn\"*G]'F-7$$\"+++]7`F*$!3Ox)[+Hm_F#F-7$$\"++++DcF*$
!3c'f!p+B#f>*F-7$$\"+++]PfF*$!3]`-)y0@\"4')F-7$$F^qF*$!38;gZp^?R**FL7$
$\"+++]ilF*$\"3a/(p\\\"*3FV(F-7$$\"++++voF*$\"3O'oihN^8z*F-7$$\"+++](=
(F*$\"3_2d95TVcTF-7$$\"+++++vF*$!3ev9Pj_vr[F-7$$\"+++]7yF*$!3x8W+_^pA*
*F-7$$\"++++D\")F*$!3Il5v?v%G(oF-7$$\"+++]P%)F*$\"3gxhCoQ#zy\"F-7$$\"+
+++]()F*$\"3;ML.jV0*)*)F-7$$\"+++]i!*F*$\"3Yk'H))z7;&))F-7$$FcqF*$\"3i
J;b&>/y[\"F-7$$\"+++](o*F*$!3%H.\\\"pYj!4(F-7$$\"+++++5!\")$!31R(3w$GN
!))*F--%&COLORG6&%$RGBG$\"\"*!\"\"Fiz$\"\"#F[[l-%&STYLEG6#%%LINEG-%*TH
ICKNESSG6#\"\"$-%%VIEWG6$;$!\"&Ffp$\"#5Ffp;Fj[l$\"\"&Ffp-%+AXESLABELSG
6$Q\"t6\"Q%y(t)Fe\\l" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 6 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }