{VERSION 4 0 "IBM INTEL NT" "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 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 1 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 1 2 2 2 2 1 1 1 1 }
1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 
-1 "Times" 1 24 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 "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 
2 1 1 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 259 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 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 256 "" 0 "" {TEXT -1 9 "John Cole" }}{PARA 256 "
" 0 "" {TEXT -1 22 "Differential Equations" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 6 "Part 3" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }{TEXT 256 148 "A.  Draw a direction field.  How do so
lutions appear to behave as t approaches 0?  Does the behavior depend \+
on the choice of the initial value of a?" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "de1 := t*diff(y(t),t
) + ((t+1)*y(t)) = 2*t*exp(-t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$
de1G/,&*&%\"tG\"\"\"-%%diffG6$-%\"yG6#F(F(F)F)*&,&F(F)F)F)F)F-F)F),$*&
F(F)-%$expG6#,$F(!\"\"F)\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "with(DEtools):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "dfieldplot(
de1, y(t), t=-10..10, y=-10..10);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 
300 300 {PLOTDATA 2 "6%-%'CURVESG6]dl7%7$$!+%>,++\"!\")$!+z:j_5F*7$$!+
b!))*****!\"*$!+5Uot%*F07$$!+<s:85F*$!+YEe,(*F07%7$$!+LESZ*)F0F+7$$!+4
ULZ*)F0$!+6Uot%*F07$$!+qz#*y!*F0$!+!3x:q*F07%7$$!+iZ$[*yF0$!+y:j_5F*7$
$!+A*QY*yF0$!+?Uot%*F07$$!+n-EE!)F0$!+e6c,(*F07%7$$!+-]QUoF0$!+s:j_5F*
7$$!+Cb#=%oF0$!+&G%ot%*F07$$!+$eDN(pF0$!+Sd^,(*F07%7$$!+x(o-z&F0$!+>:j
_5F*7$$!+\"fy')y&F0$!+6[ot%*F07$$!+t;g?fF0$!++sQ,(*F07%7$$!+**=2RZF0$!
+26j_5F*7$$!+6BhMZF0$!+M*)ot%*F07$$!+2c:n[F0$!+i3.,(*F07%7$$!+$yl-p$F0
$!+'4GE0\"F*7$$!+p_:yOF0$!+W!>PZ*F07$$!+6vM7QF0$!+o:4+(*F07%7$$!+]g0ZE
F0$!+=)3E0\"F*7$$!+W=5;EF0$!+C=\"RZ*F07$$!+qcKaFF0$!+6a%yp*F07%7$$!+rP
@=;F0$!+**[[_5F*7$$!+l4oR:F0$!+75:v%*F07$$!+jg*yo\"F0$!+*o+Ep*F07%7$$!
+U].'='!#5$!+]&Q=[*F07$$!+Q2GSVFdt$!+Xh\"=0\"F*7$$!+VY\\WMFdt$!+.>2F5F
*7%7$$\"+\"Gq))3&Fdt$!+9Fg_5F*7$$\"+>bWPaFdt$!+jG(RZ*F07$$\"+D*3p/%Fdt
$!+/@R(p*F07%7$$\"+'Qtva\"F0$!+&)z`_5F*7$$\"+_8K5;F0$!+`,iu%*F07$$\"+d
5Rl9F0$!+/GF%p*F07%7$$\"+%[IRf#F0$!+`n\\_5F*7$$\"+7uApEF0$!+uC.v%*F07$
$\"+nKo@DF0$!+lz$Hp*F07%7$$\"+mP5VOF0$!+13Z_5F*7$$\"+)G<`s$F0$!+V>Hv%*
F07$$\"+C0MwNF0$!+10A#p*F07%7$$\"+2Wf$p%F0$!+$f`C0\"F*7$$\"+0)*3!y%F0$
!+lSYv%*F07$$\"+=!H-j%F0$!+jGy\"p*F07%7$$\"+x%zZu&F0$!+m9W_5F*7$$\"+$*
y;MeF0$!+Q`ev%*F07$$\"+o5r$o&F0$!+'***[\"p*F07%7$$\"+StO'z'F0$!+mCV_5F
*7$$\"+)=Vy)oF0$!+P`nv%*F07$$\"+?p&pt'F0$!+&4!G\"p*F07%7$$\"+.%3#[yF0$
!+5bU_5F*7$$\"+$Gl7%zF0$!+'*[uv%*F07$$\"+-T0!z(F0$!+0>7\"p*F07%7$$\"+$
H>-!*)F0$!+l*>C0\"F*7$$\"+^v^%**)F0$!+`.!eZ*F07$$\"+n90V))F0$!+w\")*4p
*F07%7$$\"+(**\\B&**F0$!+NaT_5F*7$$\"++]w/5F*$!+Xc%eZ*F07$$\"+b$yf*)*F
0$!+Q')*3p*F07%7$$!+&>,++\"F*F17$F.$!+KE0@%)F07$F4$!+o5&*[')F07%7$$!+N
ESZ*)F0F17$$!+2ULZ*)F0Ff_l7$$!+pz#*y!*F0$!++b%*[')F07%7$$!+yZ$[*yF0$!+
,Uot%*F07$$!+1*QY*yF0$!+TE0@%)F07$$!+f-EE!)F0$!+v&H*[')F07%7$$!+N^QUoF
0$!+OTot%*F07$$!+\"RD=%oF0$!+1F0@%)F07$$!+3b_tpF0$!+GT))[')F07%7$$!+C)
p-z&F0$!+3Oot%*F07$$!+Wvn)y&F0$!+MK0@%)F07$$!+!3,1#fF0$!+g`v[')F07%7$$
!+s(z!RZF0$!+a%zOZ*F07$$!+QWgMZF0$!+)Qd5U)F07$$!+M6:n[F0$!+MtR[')F07%7
$$!+#o>.p$F0$!+a([OZ*F07$$!+q85yOF0$!+)3)3@%)F07$$!+'z;B\"QF0$!+noWZ')
F07%7$$!+c(etk#F0$!+0wWt%*F07$$!+Q\"*z:EF0$!+P#*G@%)F07$$!+#z^Tv#F0$!+
aK9X')F07%7$$!+YXP>;F0$!+v#H@Z*F07$$!+!>?&Q:F0$!+nvgA%)F07$$!+&)e@(o\"
F0$!+())G(R')F07%7$$!+()z!eO'Fdt$!+)oKFV)F07$$!+$z20;%Fdt$!+aT+i%*F07$
$!+e*z8N$Fdt$!+#4%f6#*F07%7$$\"+eTGp]Fdt$!+8qKt%*F07$$\"+U;.daFdt$!+H)
49U)F07$$\"+q`=eSFdt$!+O(4Vk)F07%7$$\"+Y')*Ra\"F0$!+'eADZ*F07$$\"+#4'*
Qh\"F0$!+cU@A%)F07$$\"+5VZn9F0$!+*\\v3k)F07%7$$\"+D(y&*e#F0$!+;d+s%*F0
7$$\"+r\"zNn#F0$!+E6tA%)F07$$\"+<KBCDF0$!+$o0%R')F07%7$$\"+JOKQOF0$!+o
+or%*F07$$\"+Bu4IPF0$!+un0B%)F07$$\"+.*\\\"zNF0$!+`'='Q')F07%7$$\"+)=b
&)o%F0$!+&[k9Z*F07$$\"+C!H^y%F0$!+dBFB%)F07$$\"+fh>LYF0$!+!)39Q')F07%7
$$\"+!=p&RdF0$!+KHJr%*F07$$\"+!>y$ReF0$!+5RUB%)F07$$\"+yFy'o&F0$!+7C#y
j)F07%7$$\"+Pb.\"z'F0$!+S1?r%*F07$$\"+\"*\\<$*oF0$!+-i`B%)F07$$\"+'4.,
u'F0$!+vZfP')F07%7$$\"+@ayUyF0$!+KR6r%*F07$$\"+l#)oYzF0$!+5HiB%)F07$$
\"+iiD$z(F0$!+8NUP')F07%7$$\"+!3DZ*))F0$!+P[/r%*F07$$\"+k<,+!*F0$!+0?p
B%)F07$$\"+CuHY))F0$!+4(*GP')F07%7$$\"+f%)zY**F0$!+B%))4Z*F07$$\"+a,K0
5F*$!+>%[PU)F07$$\"+'ff#**)*F0$!+X@=P')F07%7$Fc_lFf_l7$F.$!+_5UotF07$F
4$!+)[>jf(F07%7$$!+PESZ*)F0$!+JE0@%)F07$$!+0ULZ*)F0$!+`5UotF07$$!+oz#*
y!*F0$!+@RJ'f(F07%7$$!+&zM[*yF0$!+AE0@%)F07$$!+*))QY*yF0$!+i5UotF07$$!
+\\-EE!)F0$!+#*zH'f(F07%7$$!+p_QUoF0$!+dD0@%)F07$$!+d_#=%oF0$!+F6UotF0
7$$!+Ka_tpF0$!+:DD'f(F07%7$$!+u3F!z&F0$!+G?0@%)F07$$!+%\\w')y&F0$!+c;U
otF07$$!+%[+1#fF0$!+>N7'f(F07%7$$!++x3RZF0$!+Ty/@%)F07$$!+5lfMZF0$!+Ve
UotF07$$!+Jm9n[F0$!+#zjdf(F07%7$$!+]XP!p$F0$!+Nl,@%)F07$$!+-l/yOF0$!+
\\rXotF07$$!+EbG7QF0$!+N>![f(F07%7$$!+MNnZEF0$!+!\\13U)F07$$!+gV[:EF0$
!+%>n'otF07$$!+K4(Rv#F0$!+(QQCf(F07%7$$!+<eg?;F0$!+'Q,%>%)F07$$!+>*)GP
:F0$!+)Hs+P(F07$$!+$p$\\'o\"F0$!+)4Woe(F07%7$$!+%e:&HmFdt$!+oiY'Q(F07$
$!+'>+o*QFdt$!+;u+.%)F07$$!+(*Rx<KFdt$!+f3w[\")F07%7$$\"+sGuW]Fdt$!+Q#
*f?%)F07$$\"+GHd\"[&Fdt$!+YW()otF07$$\"+e/MsSFdt$!+n\">6f(F07%7$$\"+Or
]R:F0$!+'zs&>%)F07$$\"+-wQ=;F0$!+))3!*ptF07$$\"+#\\+,Z\"F0$!+k9I(e(F07
%7$$\"+0T4%e#F0$!+&=1*=%)F07$$\"+\"zj!zEF0$!+*\\n0P(F07$$\"+:*fu_#F0$!
+s#oce(F07%7$$\"+Y;HKOF0$!+zb[=%)F07$$\"+3%Hht$F0$!+0\"))4P(F07$$\"+*o
5Fe$F0$!+T#)z%e(F07%7$$\"+qR>#o%F0$!+Xy?=%)F07$$\"+U-\\\"z%F0$!+ReErtF
07$$\"+a\"fpj%F0$!+*RtUe(F07%7$$\"+l<*Ht&F0$!+eJ,=%)F07$$\"+0c&f%eF0$!
+E0YrtF07$$\"+P\"z1p&F0$!+P`#Re(F07%7$$\"+u^I%y'F0$!+'>pyT)F07$$\"+a`!
***oF0$!+)[/;P(F07$$\"+#4%4WnF0$!+?un$e(F07%7$$\"+c0%f$yF0$!+o\"exT)F0
7$$\"+IJ``zF0$!+;brrtF07$$\"+g#=tz(F0$!+A8\\$e(F07%7$$\"+$)3z()))F0$!+
^(pwT)F07$$\"+hf%p+*F0$!+LR!=P(F07$$\"+.\\T]))F0$!+ShM$e(F07%7$$\"+BCz
R**F0$!+'e(f<%)F07$$\"+e2-15F*$!+)4w=P(F07$$\"+[<U.**F0$!+Z&HKe(F07%7$
Fc_lFjbm7$$!+a!))*****F0$!+u%*y:jF07$F4$!+5zoVlF07%7$$!+RESZ*)F0Fjbm7$
$!+.ULZ*)F0Fdfn7$$!+nz#*y!*F0$!+TBoVlF07%7$$!+7[$[*yF0$!+V5UotF07$$!+s
)QY*yF0$!+$[*y:jF07$$!+R-EE!)F0$!+4kmVlF07%7$$!+.aQUoF0$!+y4UotF07$$!+
B^#=%oF0$!+[&*y:jF07$$!+c`_tpF0$!+.4iVlF07%7$$!+F>F!z&F0$!+[/UotF07$$!
+Tan)y&F0$!+y+z:jF07$$!+'))*f?fF0$!+x;\\VlF07%7$$!+%o&4RZF0$!+GiTotF07
$$!+E&)eMZF0$!+)H%z:jF07$$!+'4Ur'[F0$!+O-8VlF07%7$$!+8/V!p$F0$!+*H%Qot
F07$$!+R1*zn$F0$!+Fi#eJ'F07$$!+)o`A\"QF0$!+jn:UlF07%7$$!+>6+[EF0$!+(yk
\"otF07$$!+vn::EF0$!+Rd/;jF07$$!+lEy`FF0$!+^1tRlF07%7$$!+'=9>i\"F0$!+
\"GkmO(F07$$!+]0)f`\"F0$!+Xia<jF07$$!+#[Ddo\"F0$!+e_%R`'F07%7$$!+w1))[
qFdt$!+e!4qM'F07$$!+/^VxMFdt$!+o9?PtF07$$!+T_$H,$Fdt$!+`a<yqF07%7$$\"+
6h48]Fdt$!+um#yO(F07$$\"+*o>K^&Fdt$!+_QQ;jF07$$\"+Kij!4%Fdt$!+cjxPlF07
%7$$\"+DepL:F0$!+F@ZmtF07$$\"+8*)>C;F0$!+*RQxJ'F07$$\"+/F^t9F0$!+DI[Ll
F07%7$$\"+W3(pd#F0$!+W/eltF07$$\"+_q='o#F0$!+#3I'=jF07$$\"+aAnJDF0$!+f
%\\;`'F07%7$$\"+scWCOF0$!+(z;]O(F07$$\"+#QvRu$F0$!+HP>>jF07$$\"+d&ote$
F0$!+^)z1`'F07%7$$\"+fj\"Rn%F0$!+YekktF07$$\"+`yw*z%F0$!+!ok&>jF07$$\"
+g])=k%F0$!+`**4IlF07%7$$\"+XFVCdF0$!+$y'QktF07$$\"+DY^aeF0$!+VP#)>jF0
7$$\"+#p!y&p&F0$!+S!=(HlF07%7$$\"+'4[bx'F0$!+Gd>ktF07$$\"+KCm3pF0$!+)z
9+K'F07$$\"+;(>$\\nF0$!+4tWHlF07%7$$\"+sc.FyF0$!+9'[SO(F07$$\"+9!QC'zF
0$!+7>;?jF07$$\"+4nj-yF0$!+?ZCHlF07%7$$\"+#*3xy))F0$!+k:$RO(F07$$\"+_f
'f,*F0$!+i*y-K'F07$$\"+vd!e&))F0$!+'*p3HlF07%7$$\"+f*z1$**F0$!+xg$QO(F
07$$\"+/?$p+\"F*$!+\\WP?jF07$$\"+y3()3**F0$!+30'*GlF07%7$Fc_lFdfn7$Fbf
n$!+%*y:j_F07$F4$!+Ij0\"\\&F07%7$$!+TESZ*)F0$!+t%*y:jF07$$!+,ULZ*)F0$!
+&*y:j_F07$$!+mz#*y!*F0$!+i20\"\\&F07%7$$!+H[$[*yF0$!+k%*y:jF07$$!+b)Q
Y*yF0$!+/z:j_F07$$!+I-EE!)F0$!+E[.\"\\&F07%7$$!+PbQUoF0$!+*R*y:jF07$$!
+*)\\#=%oF0$!+pz:j_F07$$!+!GDN(pF0$!+!H*)4\\&F07%7$$!+#)HF!z&F0$!+m))y
:jF07$$!+'Qu')y&F0$!+-&eJE&F07$$!+)G*f?fF0$!+P)f3\\&F07%7$$!+EP5RZF0$!
+9Yy:jF07$$!+%[!eMZF0$!+aF;j_F07$$!+Fv8n[F0$!+nm\\!\\&F07%7$$!+(H([!p$
F0$!+W?v:jF07$$!+bP$zn$F0$!+C`>j_F07$$!+m7A7QF0$!+Y8^*[&F07%7$$!+5BM[E
F0$!+YC_:jF07$$!+%e:[h#F0$!+A\\Uj_F07$$!+Cle`FF0$!+x)>q[&F07%7$$!++rIB
;F0$!+Xn\"RJ'F07$$!+OweM:F0$!+B1.l_F07$$!+Gn!\\o\"F0$!+(>J5[&F07%7$$!+
\"=?@z(Fdt$!+I$)*yK&F07$$!+*f&>MFFdt$!+Q!\\5D'F07$$!+4+LvEFdt$!+!*p&z)
fF07%7$$\"+G7uq\\Fdt$!+Cl(\\J'F07$$\"+sXdbbFdt$!+W3(RE&F07$$\"+Qt>:TFd
t$!+K)4U[&F07%7$$\"+?j)e_\"F0$!+Tz58jF07$$\"+=%3?j\"F0$!+F%ReE&F07$$\"
+YP7y9F0$!+\\WJzaF07%7$$\"+s@NnDF0$!+]f&=J'F07$$\"+Cd!ep#F0$!+=94n_F07
$$\"+[\"*RPDF0$!+!)GBxaF07%7$$\"+R9$Qh$F0$!+$pi5J'F07$$\"+:'*eaPF0$!+v
Y)yE&F07$$\"+Ctr$f$F0$!+pX9waF07%7$$\"+hJriYF0$!+yHa5jF07$$\"+^5(4\"[F
0$!+!R/%o_F07$$\"+_\\g[YF0$!+x<]vaF07%7$$\"+\"H\\Gr&F0$!+o==5jF07$$\"+
z!)4meF0$!++bwo_F07$$\"+(pTFq&F0$!+fE3vaF07%7$$\"+1*)pjnF0$!+Gl\"*4jF0
7$$\"+A;^?pF0$!+S3.p_F07$$\"+i*\\kv'F0$!+7wyuaF07%7$$\"+R!*)\\\"yF0$!+
mEr4jF07$$\"+ZY[uzF0$!+-ZBp_F07$$\"+*3$*)4yF0$!+QycuaF07%7$$\"+()3dm))
F0$!+n1b4jF07$$\"+df;G!*F0$!+,nRp_F07$$\"+_.;j))F0$!+dsRuaF07%7$$\"+@p
N=**F0$!+-'=%4jF07$$\"+3V;35F*$!+m(G&p_F07$$\"+gVI;**F0$!+]2EuaF07%7$F
c_lFhio7$Fbfn$!+;j_5UF07$F4$!+_ZUQWF07%7$$!+VESZ*)F0Fhio7$$!+*>Mt%*)F0
F`]q7$$!+lz#*y!*F0$!+#=>%QWF07%7$$!+X[$[*yF0$!+')y:j_F07$$!+R)QY*yF0$!
+Cj_5UF07$$!+@-EE!)F0$!+TKSQWF07%7$$!+rcQUoF0$!+?y:j_F07$$!+b[#=%oF0$!
+!RE0@%F07$$!+/__tpF0$!+ywNQWF07%7$$!+TSF!z&F0$!+'GdJE&F07$$!+FLn)y&F0
$!+Cp_5UF07$$!+(o)f?fF0$!+$*zAQWF07%7$$!+D=6RZF0$!++I:j_F07$$!+&QsXt%F
0$!+57`5UF07$$!+EH8n[F0$!+$3jyV%F07%7$$!+J_a!p$F0$!+r(>JE&F07$$!+@e(yn
$F0$!+RWc5UF07$$!+X#)=7QF0$!+xc'oV%F07%7$$!+szp[EF0$!+8%zGE&F07$$!+A*f
Wh#F0$!+(z/3@%F07$$!+/?Q`FF0$!+xeIMWF07%7$$!+&*HzC;F0$!+it:h_F07$$!+T<
5L:F0$!+[o_7UF07$$!+%HKSo\"F0$!+215GWF07%7$$!+Zkh=#*Fdt$!+Akj*Q%F07$$!
+L$*p28Fdt$!+)yZS3&F07$$!+A*[C:#Fdt$!+`o\"[$[F07%7$$\"+e8:6\\Fdt$!+W%z
>E&F07$$\"+UW;:cFdt$!+mZq6UF07$$\"+#z(*)\\TFdt$!+SdHIWF07%7$$\"+ZM%[^
\"F0$!+h%R#f_F07$$\"+\"H^Ik\"F0$!+\\ZW9UF07$$\"+STp%[\"F0$!+fMiCWF07%7
$$\"+Xim`DF0$!+!3ftD&F07$$\"+^;\\4FF0$!+I^K;UF07$$\"+<_iXDF0$!+;uBAWF0
7%7$$\"+GVp)f$F0$!+dS;c_F07$$\"+EnspPF0$!+`,_<UF07$$\"+Pm'Gg$F0$!+0T,@
WF07%7$$\"+)3Hnk%F0$!+xhQb_F07$$\"+C^&p#[F0$!+L!)H=UF07$$\"+C!*HeYF0$!
+[fI?WF07%7$$\"+5gK'p&F0$!+a'\\[D&F07$$\"+g8i#)eF0$!+cX$)=UF07$$\"+Y`y
7dF0$!+'[^)>WF07%7$$\"+,F!ou'F0$!+LvXa_F07$$\"+FySPpF0$!+xmA>UF07$$\"+
]ntmnF0$!+\"4N&>WF07%7$$\"+hv\"yz(F0$!+as:a_F07$$\"+Dhl\"*zF0$!+cp_>UF
07$$\"+e+O?yF0$!+m6I>WF07%7$$\"+.k=\\))F0$!+$3>RD&F07$$\"+T/bX!*F0$!+F
^w>UF07$$\"+Nrwt))F0$!+A07>WF07%7$$\"+d>!3!**F0$!+F^s`_F07$$\"+/)>*45F
*$!+$3f*>UF07$$\"+sK-F**F0$!+'[w*=WF07%7$Fc_l$!+:j_5UF07$Fbfn$!+PZ*y:$
F07$F4$!+sJz&Q$F07%7$$!+XESZ*)F0$!+9j_5UF07$$!+(>Mt%*)F0$!+QZ*y:$F07$$
!+kz#*y!*F0$!+/wy&Q$F07%7$$!+i[$[*yF0$!+1j_5UF07$$!+A)QY*yF0$!+YZ*y:$F
07$$!+6-EE!)F0$!+f;x&Q$F07%7$$!+1eQUoF0$!+Ti_5UF07$$!+?Z#=%oF0$!+6[*y:
$F07$$!+F^_tpF0$!+lgs&Q$F07%7$$!+-^F!z&F0$!+0d_5UF07$$!+mAn)y&F0$!+Z`*
y:$F07$$!+&3)f?fF0$!+]hf&Q$F07%7$$!+#)*>\"RZF0$!+'Q@0@%F07$$!+GUcMZF0$
!+m'**y:$F07$$!+$HGr'[F0$!+%[H_Q$F07%7$$!+WUg!p$F0$!+yu[5UF07$$!+3o\"y
n$F0$!+uN$z:$F07$$!+2Y:7QF0$!+](>UQ$F07%7$$!+W!p!\\EF0$!+FcB5UF07$$!+]
))39EF0$!+Da=eJF07$$!+f&oJv#F0$!+^%)e\"Q$F07%7$$!+j9QE;F0$!+kWQ3UF07$$
!+tK^J:F0$!+)eO+;$F07$$!+Bj4$o\"F0$!+P?:vLF07%7$$!+]@O^5F0$!+1Ju?PF07$
$!)#G%p7Fdt$!+YznZOF07$$!+kJaxBFdt$!+FaBKNF07%7$$\"+6l;@[Fdt$!+Yrm3UF0
7$$\"+*G\\^q&Fdt$!+1RvfJF07$$\"+_)>E?%Fdt$!+*\\+eP$F07%7$$\"+3c1)\\\"F
0$!+<WF/UF07$$\"+I\"H)f;F0$!+Nm9kJF07$$\"+F.z%\\\"F0$!+l/7pLF07%7$$\"+
H;qKDF0$!+'*\\:,UF07$$\"+niXIFF0$!+cgEnJF07$$\"+9]SeDF0$!+[-RmLF07%7$$
\"+-HWvNF0$!+5[;*>%F07$$\"+_\"yHz$F0$!+UiDpJF07$$\"+==9<OF0$!+#3Y]O$F0
7%7$$\"+L4<AYF0$!+QC)y>%F07$$\"+zK^^[F0$!+9'Q0<$F07$$\"+F7WtYF0$!+$G(H
kLF07%7$$\"+dT&4n&F0$!+y\"3q>%F07$$\"+8K*z!fF0$!+uGTrJF07$$\"+RLZGdF0$
!+*)3$QO$F07%7$$\"+hu(3s'F0$!+*ouj>%F07$$\"+nILjpF0$!+jj/sJF07$$\"+[))
z#y'F0$!++I^jLF07%7$$\"+_#)[rxF0$!+h@*e>%F07$$\"+Ma)z,)F0$!+\"*)GD<$F0
7$$\"+?opOyF0$!+!R\"GjLF07%7$$\"+qkaA))F0$!+C1^&>%F07$$\"+u.>s!*F0$!+G
/\"H<$F07$$\"+feJ!*))F0$!+xV5jLF07%7$$\"+&R9R()*F0$!+y/?&>%F07$$\"+g&3
E,\"F*$!+u0AtJF07$$\"+W9uV**F0$!+7V'HO$F07%7$Fc_l$!+OZ*y:$F07$$!+`!))*
****F0$!+eJE0@F07$F4$!+$fhJL#F07%7$$!+ZESZ*)F0$!+NZ*y:$F07$$!+&>Mt%*)F
0$!+fJE0@F07$$!+iz#*y!*F0$!+Cg:LBF07%7$$!+z[$[*yF0$!+FZ*y:$F07$$!+0)QY
*yF0$!+nJE0@F07$$!+,-EE!)F0$!+w+9LBF07%7$$!+SfQUoF0$!+iY*y:$F07$$!+'eC
=%oF0$!+KKE0@F07$$!+^]_tpF0$!+_W4LBF07%7$$!+mhF!z&F0$!+DT*y:$F07$$!+-7
n)y&F0$!+pPE0@F07$$!+\"[(f?fF0$!+1V'HL#F07%7$$!+)>G\"RZF0$!+s(*)y:$F07
$$!+7gbMZF0$!+A\"o_5#F07$$!+EO7n[F0$!+refKBF07%7$$!+nVm!p$F0$!+m^&y:$F
07$$!+&ocxn$F0$!+GFI0@F07$$!+N.77QF0$!+bNdJBF07%7$$!+\\lX\\EF0$!+@5fdJ
F07$$!+X8q8EF0$!+toc0@F07$$!+#fXHv#F0$!+#Qn)GBF07%7$$!+cM3G;F0$!+!3'fb
JF07$$!+!G6)H:F0$!+9=c2@F07$$!+8@4#o\"F0$!+nQ=ABF07%7$$!+B+P`*)Fdt$!+&
Qao+$F07$$!+dd%Hd\"Fdt$!+4NIcAF07$$!+xI/4TFdt$!+PsaEBF07%7$$\"+I2xpYFd
t$!+5!RX:$F07$$\"+q]aceFdt$!+%))='3@F07$$\"+K2?#H%Fdt$!+aDB?BF07%7$$\"
+>Nlp9F0$!+,=UYJF07$$\"+>7C)o\"F0$!+$4On6#F07$$\"+!)[?7:F0$!+EhM7BF07%
7$$\"+1I#o\\#F0$!+U6NSJF07$$\"+!*[LmFF0$!+_n!G7#F07$$\"+23z!e#F0$!+*eA
%4BF07%7$$\"+P\\aNNF0$!+c>YOJF07$$\"+<h(G$QF0$!+QfpE@F07$$\"+w7GUOF0$!
+(H]\"3BF07%7$$\"+$fj+e%F0$!+%)=+MJF07$$\"+>1i$*[F0$!+5g:H@F07$$\"+(zF
,q%F0$!+&*o^2BF07%7$$\"+0j_FcF0$!+%pfB8$F07$$\"+l5U^fF0$!++#)zI@F07$$
\"+115cdF0$!+zd:2BF07%7$$\"+*4!ewmF0$!+C&)=JJF07$$\"+H/j2qF0$!+q$p>8#F
07$$\"+ON06oF0$!+s`#pI#F07%7$$\"+.'pls(F0$!+:aIIJF07$$\"+$3/H1)F0$!+zC
&G8#F07$$\"+:RSlyF0$!+kbw1BF07%7$$\"+<m:x()F0$!+F8hHJF07$$\"+F-e<\"*F0
$!+nlaL@F07$$\"+e#o$>*)F0$!+izk1BF07%7$$\"+^?:G)*F0$!+S\"\\!HJF07$$\"+
&z%=<5F*$!+a(3T8#F07$$\"+d!oI(**F0$!+zwb1BF07%7$Fc_lFbds7$F`ds$FKF07$F
4$!+8+`!G\"F07%7$$!+\\ESZ*)F0$!+cJE0@F07$$!+$>Mt%*)F0$!+!eJE0\"F07$$!+
hz#*y!*F0$!+XW_!G\"F07%7$$!+'*[$[*yF0$!+[JE0@F07$$!+)yQY*yF0$!+)eJE0\"
F07$$!+#>gi-)F0$!+$\\30G\"F07%7$$!+vgQUoF0$!+$3j_5#F07$$!+^W#=%oF0$!+`
;j_5F07$$!+v\\_tpF0$!+SGY!G\"F07%7$$!+LsF!z&F0$!+WDE0@F07$$!+N,n)y&F0$
!+#>KE0\"F07$$!+wof?fF0$!+hCL!G\"F07%7$$!+uk8RZF0$!+d\"e_5#F07$$!+OxaM
ZF0$!+zlj_5F07$$!+C*=r'[F0$!+VA'*z7F07%7$$!+Kcs!p$F0$!+KGA0@F07$$!+?ap
xOF0$!+/>n_5F07$$!+4a37QF0$!+)3F*y7F07%7$$!+/;')\\EF0$!+>b%\\5#F07$$!+
!H'H8EF0$!+<#\\H0\"F07$$!+]Cr_FF0$!+LC9w7F07%7$$!+N:\"*H;F0$!+n)*y-@F0
7$$!+,K)z_\"F0$!+p[5b5F07$$!+e>,\"o\"F0$!+$G%>p7F07%7$$!+$eL4l(Fdt$!+.
@)z/#F07$$!+(>#QvGFdt$!+LE\"*46F07$$!+Ri!>3&Fdt$!+RiJ`7F07%7$$\"+L#eHO
%Fdt$!+-w](4#F07$$\"+nvNjhFdt$!+MrQg5F07$$\"+#4frZ%Fdt$!+5`Ui7F07%7$$
\"+4y279F0$!+E&4\"y?F07$$\"+Hp\"eu\"F0$!+5_yz5F07$$\"+](p([:F0$!+v8@a7
F07%7$$\"+m`YBCF0$!+#fpB1#F07$$\"+IDpRGF0$!+W^_&4\"F07$$\"+\\6sGEF0$!+
7Z#GD\"F07%7$$\"+uU;aMF0$!+'oDB0#F07$$\"+!ycU\"RF0$!+]!pb5\"F07$$\"+^#
*H'p$F0$!+6j.`7F07%7$$\"+3Gp%\\%F0$!+(H]i/#F07$$\"+/9**y\\F0$!+RWk66F0
7$$\"+]>JdZF0$!+=_X`7F07%7$$\"+__,SbF0$!+1(*QU?F07$$\"+=@$*QgF0$!+I]]:
6F07$$\"+jG0:eF0$!+So\"QD\"F07%7$$\"+hVy(e'F0$!+#GR(R?F07$$\"+nhU'4(F0
$!+aa:=6F07$$\"+2S5roF0$!+!)R5a7F07%7$$\"+3c\"pj(F0$!+c**yP?F07$$\"+y!
eD:)F0$!+!y/,7\"F07$$\"+hv?EzF0$!+STLa7F07%7$$\"+i+)oo)F0$!+!3\"GO?F07
$$\"+#ycy?*F0$!+cOh@6F07$$\"+&eG2)*)F0$!+sG_a7F07%7$$\"+XuRP(*F0$!+(Qq
].#F07$$\"+c-EE5F*$!+\\V#G7\"F07$$\"+ch[.5F*$!+r2oa7F07%7$Fc_lFjgt7$F`
ds$\"\"$Fdt7$F4$!+\\V)*yAFdt7%7$$!+^ESZ*)F0$!+x:j_5F07$$!+\">Mt%*)F0$!
\"(Fdt7$$!+gz#*y!*F0$!+Z'G*yAFdt7%7$$!+8\\$[*yF0$!+p:j_5F07$$!+r(QY*yF
0$!#))Fdt7$$!+#=gi-)F0$!+#4p(yAFdt7%7$$!+4iQUoF0$!+/:j_5F07$$!+<V#=%oF
0$!$X(Fdt7$$!+**[_tpF0$!+vAJyAFdt7%7$$!+.$y-z&F0$!+k4j_5F07$$!+l!p')y&
F0$!%WhFdt7$$!+pif?fF0$!+ah+xAFdt7%7$$!+4[9RZF0$!+Tli_5F07$$!+,%RXt%F0
$!&o.&Fdt7$$!+*=9r'[F0$!+9gGtAFdt7%7$$!+q!)y!p$F0$!+w/f_5F07$$!+#)HjxO
F0$!'>5TFdt7$$!+9)\\?\"QF0$!+,M!GE#Fdt7%7$$!+GaG]EF0$!+Q!*H_5F07$$!+mC
(Gh#F0$!(.aK$Fdt7$$!+A%oCv#F0$!+zM8MAFdt7%7$$!+v,)=j\"F0$!+DI'*\\5F07$
$!+hX,E:F0$!)EboEFdt7$$!+[p%)z;F0$!+cD\"=;#Fdt7%7$$!+:1uspFdt$!+DC4C5F
07$$!+l^d`NFdt$!*H:R&GFdt7$$!+!z(GQbFdt$!+3>V8?Fdt7%7$$\"+(Ri)RMFdt$!+
d1/?5F07$$\"+.MX'3(Fdt$!*4#4fKFdt7$$\"+@6ji]Fdt$!+Bn(z+#Fdt7%7$$\"+g%o
OD\"F0$!+IN\"3S*Fdt7$$\"+yiA/>F0$!+]A]D6Fdt7$$\"+))\\$*f;F0$!+FC'R5#Fd
t7%7$$\"+q=bMAF0$!+&Gn#=()Fdt7$$\"+EggGIF0$!+&\\[!3=Fdt7$$\"+B0JqFF0$!
+aqe6BFdt7%7$$\"+qq'pD$F0$!+.pxO$)Fdt7$$\"+%)RX6TF0$!+x)Q&*=#Fdt7$$\"+
l;h\\QF0$!+2jM_CFdt7%7$$\"+Lkb'H%F0$!+.1&o9)Fdt7$$\"+zx7x^F0$!+x^YzBFd
t7$$\"+shQ9\\F0$!+olUFDFdt7%7$$\"+#pEGM&F0$!+1aIZ!)Fdt7$$\"+y17OiF0$!+
u.,zCFdt7$$\"+pJ6tfF0$!+IT'zc#Fdt7%7$$\"+(Gk=R'F0$!+vA!)))zFdt7$$\"+Ti
M#H(F0$!+0N^PDFdt7$$\"+q]CHqF0$!+-(\\@f#Fdt7%7$$\"+:t<UuF0$!+p)H,&zFdt
7$$\"+rjHZ$)F0$!+6f=wDFdt7$$\"+[!eT3)F0$!+)3!G3EFdt7%7$$\"+Rp:$\\)F0$!
+O&4@#zFdt7$$\"+0*z:S*F0$!+Wi?/EFdt7$$\"+snUQ\"*F0$!+st.?EFdt7%7$$\"+:
/`W&*F0$!+J1]+zFdt7$$\"+fpaX5F*$!+\\^\"ei#Fdt7$$\"+\">J#>5F*$!+#4W\"HE
Fdt7%7$Fc_l$\"\"(Fdt7$F`ds$\"+z:j_5F07$F4$\"+Q9LZ#)Fdt7%7$$!+`ESZ*)F0$
\"#:Fdt7$$!+*=Mt%*)F0$\"+y:j_5F07$$!+fz#*y!*F0$\"+WrQZ#)Fdt7%7$$!+H\\$
[*yF0$\"#(*Fdt7$$!+b(QY*yF0$\"+q:j_5F07$$!+t,EE!)F0$\"+OnaZ#)Fdt7%7$$!
+WjQUoF0$\"$c(Fdt7$$!+#=C=%oF0$\"+/:j_5F07$$!+A[_tpF0$\"+[Q+[#)Fdt7%7$
$!+w$z-z&F0$\"%shFdt7$$!+#*zm)y&F0$\"+j4j_5F07$$!+gcf?fF0$\"+3BJ\\#)Fd
t7%7$$!+1K:RZF0$\"&Y2&Fdt7$$!+/5`MZF0$\"+0li_5F07$$!+>%4r'[F0$\"+_00`#
)Fdt7%7$$!+<<&3p$F0$\"'@!>%Fdt7$$!+N$pvn$F0$\"+y'*e_5F07$$!+FN,7QF0$\"
+wpmj#)Fdt7%7$$!+a$H2l#F0$\"(p^[$Fdt7$$!+S&GCh#F0$\"+jIG_5F07$$!+GF@_F
F0$\"+Y:?$H)Fdt7%7$$!+Sh+M;F0$\")!=y)GFdt7$$!+'f))Q_\"F0$\"+iPu\\5F07$
$!+Oney;F0$\"+W\\do$)Fdt7%7$$!+#e)R$e'Fdt$\"*_&y#o\"Fdt7$$!+)><H%RFdt$
\"+DP!e.\"F07$$!+C!=$)y&Fdt$\"+^*\\>[)Fdt7%7$$\"*m\"3uGFdt$\"+t6gypFdt
7$$\"+j2*Q-\"F0$\"+FYrZNFdt7$$\"+7c?8&)Fdt$\"+(ygW`&Fdt7%7$$\"+-#)\\)4
\"F0$\"+\">R?T(Fdt7$$\"+OlRf?F0$\"+4mF9JFdt7$$\"+wz20>F0$\"+@C*eC&Fdt7
%7$$\"+D6xw@F0$\"+jj*=\"zFdt7$$\"+rnQ'3$F0$\"+P%>Wh#Fdt7$$\"+owmbHF0$
\"+$Rw$)*[Fdt7%7$$\"+!z!oOKF0$\"+<P4L!)Fdt7$$\"+k-uJTF0$\"+$3AK\\#Fdt7
$$\"+)f-s+%F0$\"+>QY6[Fdt7%7$$\"+JP]*G%F0$\"+@J=O!)Fdt7$$\"+\"[!=%=&F0
$\"+zE8!\\#Fdt7$$\"+8H!)f]F0$\"+fPB4[Fdt7%7$$\"+,pPS`F0$\"+JRh2!)Fdt7$
$\"+p/dQiF0$\"+p=q=DFdt7$$\"+esr7hF0$\"+^\"G)H[Fdt7%7$$\"+))G,\"R'F0$
\"+M%)ouzFdt7$$\"+Sw>$H(F0$\"+mti^DFdt7$$\"+vrllrF0$\"+qa[`[Fdt7%7$$\"
+F7)=W(F0$\"+sm8XzFdt7$$\"+fCfZ$)F0$\"+G\"z6e#Fdt7$$\"+%p\\&=#)F0$\"+U
!\\Y([Fdt7%7$$\"+6R0$\\)F0$\"+/)[.#zFdt7$$\"+LHo,%*F0$\"+'*p'fg#Fdt7$$
\"+_()Qr#*F0$\"+'o]B*[Fdt7%7$$\"+[X\\W&*F0$\"+I6))**yFdt7$$\"+X0bX5F*$
\"+qYVEEFdt7$$\"+)Q=C.\"F*$\"+]H$p!\\Fdt7%7$Fc_l$\"+!eJE0\"F07$$!+_!))
*****F0$\"+eJE0@F07$F4$\"+BZOx=F07%7$$!+bESZ*)F0Fbbx7$$!+(=Mt%*)F0Fgbx
7$$!+ez#*y!*F0$\"+&Hqt(=F07%7$$!+Y\\$[*yF0$\"+)eJE0\"F07$$!+Q(QY*yF0$
\"+]JE0@F07$$!+j,EE!)F0$\"+eiQx=F07%7$$!+zkQUoF0$\"+a;j_5F07$$!+ZS#=%o
F0$\"+%3j_5#F07$$!+YZ_tpF0$\"+)*>Vx=F07%7$$!+^/G!z&F0$\"+)>KE0\"F07$$!
+<pm)y&F0$\"+SDE0@F07$$!+]]f?fF0$\"+yIcx=F07%7$$!+k;;RZF0$\"+\"pOE0\"F
07$$!+YD_MZF0$\"+Z!e_5#F07$$!+9Y5n[F0$\"+G(Qz(=F07%7$$!+3m\"4p$F0$\"+/
Vn_5F07$$!+WW]xOF0$\"+M/A0@F07$$!+Hl(>\"QF0$\"+LS,z=F07%7$$!+Z[>^EF0$
\"+^s*H0\"F07$$!+ZI'>h#F0$\"+([(*[5#F07$$!+5X%>v#F0$\"+!Qe?)=F07%7$$!+
b*3jj\"F0$\"+_nwb5F07$$!+\"y&e@:F0$\"+')z7-@F07$$!+J#>sn\"F0$\"+IX#**)
=F07%7$$!+bmANjFdt$\"+(*emj5F07$$!+D\"*3\">%Fdt$\"+T)GU4#F07$$!+*>7N%f
Fdt$\"+Qr!z*=F07%7$$\"+hH-xPFdt$\"+:d%Q3#F07$$\"+RGH\\nFdt$\"+B!\\S2\"
F07$$\"+)RB!otFdt$\"+$zH)H8F07%7$$\"+g<Qe8F0$\"+En\"o0#F07$$\"+yH^*z\"
F0$\"+7!y55\"F07$$\"+2EZB=F0$\"+;H9j8F07%7$$\"+1.Y*R#F0$\"+bHJ^?F07$$
\"+!f(pjGF0$\"+$y\"e16F07$$\"+m'y7)GF0$\"+U<:p8F07%7$$\"+TCvWMF0$\"+U]
jZ?F07$$\"+8'oO#RF0$\"+'pf-6\"F07$$\"+R@:PRF0$\"+L>2t8F07%7$$\"+?3=\"
\\%F0$\"+KOTW?F07$$\"+#R.D)\\F0$\"+16[86F07$$\"+,b\\#*\\F0$\"+K#\\kP\"
F07%7$$\"+6btQbF0$\"+v&)pT?F07$$\"+f=@SgF0$\"+jh>;6F07$$\"+YoKZgF0$\"+
cyDz8F07%7$$\"+!4Cte'F0$\"+]\\[R?F07$$\"+Qk)o4(F0$\"+)y4%=6F07$$\"+\\t
p,rF0$\"+/P_\"Q\"F07%7$$\"+v8vOwF0$\"+PwpP?F07$$\"+6Bs_\")F0$\"+,r>?6F
07$$\"+$*))pb\")F0$\"+h\"QLQ\"F07%7$$\"+i<#oo)F0$\"+qyCO?F07$$\"+#3:z?
*F0$\"+ook@6F07$$\"+%>?%4#*F0$\"+e/![Q\"F07%7$$\"+BoPP(*F0$\"+:&e].#F0
7$$\"+=BEE5F*$\"+Bi$G7\"F07$$\"+zJHE5F*$\"+PR*fQ\"F07%7$Fc_l$\"+fJE0@F
07$Febx$\"+PZ*y:$F07$F4$\"+-j**HHF07%7$$!+eESZ*)F0$\"+gJE0@F07$$!+%=Mt
%*)F0$\"+OZ*y:$F07$$!+cz#*y!*F0$\"+u=+IHF07%7$$!+j\\$[*yF0$\"+oJE0@F07
$$!+@(QY*yF0$\"+GZ*y:$F07$$!+a,EE!)F0$\"+Sy,IHF07%7$$!+9mQUoF0$\"+MKE0
@F07$$!+7R#=%oF0$\"+iY*y:$F07$$!+pY_tpF0$\"+5O1IHF07%7$$!+H:G!z&F0$\"+
zPE0@F07$$!+Rem)y&F0$\"+<T*y:$F07$$!+RWf?fF0$\"+D\\>IHF07%7$$!+%=q\"RZ
F0$\"+2$o_5#F07$$!+ES^MZF0$\"+*e*)y:$F07$$!+u(*4n[F0$\"+;CdIHF07%7$$!+
zF)4p$F0$\"+InI0@F07$$!+t#Qun$F0$\"+m6&y:$F07$$!+*zQ>\"QF0$\"+u;mJHF07
%7$$!+<No^EF0$\"+#GZc5#F07$$!+xVZ6EF0$\"+91^dJF07$$!+FGm^FF0$\"+l;![$H
F07%7$$!+#\\6)Q;F0$\"+p(y'3@F07$$!+WK3>:F0$\"+F\"zW:$F07$$!+:-tv;F0$\"
+RF-VHF07%7$$!+?pPkhFdt$\"+?k.8@F07$$!+g)Q>O%Fdt$\"+w97]JF07$$!+mW`[gF
dt$\"+^k6[HF07%7$$\"+U5!oX%Fdt$\"+]5o^JF07$$\"+eZ^pgFdt$\"+YoZ6@F07$$
\"+^sg?qFdt$\"+%eYoN#F07%7$$\"+jtxZ9F0$\"+LuGTJF07$$\"+vt65<F0$\"+j/(=
7#F07$$\"+<iu!y\"F0$\"+8KPvBF07%7$$\"+*o:l[#F0$\"+Y(3v8$F07$$\"+2AkwFF
0$\"+]\"\\c7#F07$$\"+B/JSGF0$\"+%**))4Q#F07%7$$\"+V(*QJNF0$\"+6)>_8$F0
7$$\"+68.PQF0$\"+&3Qz7#F07$$\"+'=on*QF0$\"+shA%Q#F07%7$$\"+#R&[yXF0$\"
+$p1N8$F07$$\"+?))>&*[F0$\"+.7lH@F07$$\"+)G5@&\\F0$\"+r9e'Q#F07%7$$\"+
kS%pi&F0$\"+I5<KJF07$$\"+1L+_fF0$\"+mo)48#F07$$\"+ORx1gF0$\"+,?Q)Q#F07
%7$$\"+p(ojn'F0$\"+g%=68$F07$$\"+f<%y+(F0$\"+O%R?8#F07$$\"+I1'41(F0$\"
+90y*Q#F07%7$$\"+lO\\ExF0$\"+.)z-8$F07$$\"+@+)H1)F0$\"+$4yG8#F07$$\"+-
Q![6)F0$\"+#p#)3R#F07%7$$\"+5&Hrx)F0$\"+j?gHJF07$$\"+Mtg<\"*F0$\"+LebL
@F07$$\"+-vRo\"*F0$\"+'*ew\"R#F07%7$$\"+?C9G)*F0$\"+9e/HJF07$$\"+ed=<5
F*$\"+#37T8#F07$$\"+y2=A5F*$\"+\\f[#R#F07%7$Fc_l$\"+QZ*y:$F07$Febx$\"+
;j_5UF07$F4$\"+\")yi#)RF07%7$$!+gESZ*)F0$\"+RZ*y:$F07$$!+#=Mt%*)F0$\"+
:j_5UF07$$!+bz#*y!*F0$\"+`Mj#)RF07%7$$!+!)\\$[*yF0$\"+ZZ*y:$F07$$!+/(Q
Y*yF0$\"+2j_5UF07$$!+W,EE!)F0$\"+B%\\E)RF07%7$$!+]nQUoF0$\"+8[*y:$F07$
$!+wP#=%oF0$\"+Ti_5UF07$$!+#fCN(pF0$\"+B_p#)RF07%7$$!+6EG!z&F0$\"+f`*y
:$F07$$!+dZm)y&F0$\"+&pD0@%F07$$!+CQf?fF0$\"+un#G)RF07%7$$!+n(y\"RZF0$
\"+D***y:$F07$$!+Va]MZF0$\"+H6_5UF07$$!+)*[4n[F0$\"+=h?$)RF07%7$$!+p-0
\"p$F0$\"+#=Rz:$F07$$!+$yqtn$F0$\"+s=[5UF07$$!+:.!>\"QF0$\"+J'4V)RF07%
7$$!+Or>_EF0$\"+Z()HeJF07$$!+e2'4h#F0$\"+2B75UF07$$!+TmO^FF0$\"+t.b()R
F07%7$$!+92aT;F0$\"+B+jhJF07$$!+ASN;:F0$\"+J5z1UF07$$!+iG5u;F0$\"+r`:'
*RF07%7$$!+zi'*RgFdt$\"+**)eO;$F07$$!+,&\\j[%Fdt$\"+b@w/UF07$$!+sk4ChF
dt$\"+)*ox)*RF07%7$$\"+JwL7ZFdt$\"+_gj2UF07$$\"+p\"yR\"eFdt$\"+-]ygJF0
7$$\"+5)HS)oFdt$\"+5a?,MF07%7$$\"+A&3l[\"F0$\"+O]M-UF07$$\"+;iQr;F0$\"
+=g2mJF07$$\"+[E*3w\"F0$\"+aXa8MF07%7$$\"+H5;FDF0$\"+\"Rk+?%F07$$\"+no
*ft#F0$\"+jmNoJF07$$\"+[gu>GF0$\"+=C$yT$F07%7$$\"+1')=tNF0$\"+/No)>%F0
7$$\"+[CB&z$F0$\"+]vtpJF07$$\"+!zwd(QF0$\"+kjE?MF07%7$$\"+^'48i%F0$\"+
4%*o(>%F07$$\"+hXP_[F0$\"+X;tqJF07$$\"+hsrI\\F0$\"+Pw&>U$F07%7$$\"+#3N
1n&F0$\"+HV$p>%F07$$\"+)G7$3fF0$\"+Dn[rJF07$$\"+9Y.&)fF0$\"+%H7KU$F07%
7$$\"+!Hh2s'F0$\"+zrM'>%F07$$\"+Q#\\M'pF0$\"+vQ2sJF07$$\"+>*R*QqF0$\"+
W:<CMF07%7$$\"+3kWrxF0$\"+\"3#)e>%F07$$\"+ys-=!)F0$\"+t*QD<$F07$$\"+U)
eD4)F0$\"+k=#\\U$F07%7$$\"+0:`A))F0$\"+sp]&>%F07$$\"+R`?s!*F0$\"+#39H<
$F07$$\"+zM(f9*F0$\"+m6_DMF07%7$$\"+q!4R()*F0$\"+k\"*>&>%F07$$\"+$44E,
\"F*$\"+!*=AtJF07$$\"+6R#*>5F*$\"+$>4gU$F07%7$Fc_l$\"+<j_5UF07$$!+^!))
*****F0$\"+&*y:j_F07$F4$\"+g%f_.&F07%7$$!+iESZ*)F0$\"+=j_5UF07$$!+!=Mt
%*)F0$\"+%*y:j_F07$$!+az#*y!*F0$\"+L]EN]F07%7$$!+(*\\$[*yF0$\"+Ej_5UF0
7$$!+(oQY*yF0$\"+')y:j_F07$$!+M,EE!)F0$\"+15GN]F07%7$$!+&)oQUoF0$\"+#R
E0@%F07$$!+TO#=%oF0$\"+?y:j_F07$$!+:X_tpF0$\"+OoKN]F07%7$$!+&p$G!z&F0$
\"+Sp_5UF07$$!+tOm)y&F0$\"+ss:j_F07$$!+5Kf?fF0$\"+A'ea.&F07%7$$!+8u=RZ
F0$\"+U:`5UF07$$!+(z'\\MZF0$\"+qE:j_F07$$!+')**3n[F0$\"+Q)Re.&F07%7$$!
+=\">6p$F0$\"+h;d5UF07$$!+M>IxOF0$\"+^D6j_F07$$!+`5'=\"QF0$\"+6z&p.&F0
7%7$$!+mwt_EF0$\"+&z^4@%F07$$!+G-U5EF0$\"+<Cti_F07$$!++[0^FF0$\"+7\\IS
]F07%7$$!+A'GXk\"F0$\"+c\"GY@%F07$$!+9hO8:F0$\"+cg0f_F07$$!+=rJs;F0$\"
+'4E$\\]F07%7$$!+*yxa%fFdt$\"+#)y'\\@%F07$$!+\"*z$3e%Fdt$\"+Ijre_F07$$
!+Mn(4='Fdt$\"+ghz\\]F07%7$$\"+BFGX[Fdt$\"+'Q'\\h_F07$$\"+xI.\"o&Fdt$
\"+Ey=7UF07$$\"+=Ns6oFdt$\"+tm\")\\WF07%7$$\"+j0v2:F0$\"+E,Ke_F07$$\"+
vT9];F0$\"+'3k`@%F07$$\"+fXo\\<F0$\"+%*)p*eWF07%7$$\"+J+C]DF0$\"+$pMoD
&F07$$\"+ly\"Hr#F0$\"+>&\\o@%F07$$\"+G_p2GF0$\"+VwMiWF07%7$$\"+oYH(f$F
0$\"+R;$fD&F07$$\"+'QE6x$F0$\"+tDv<UF07$$\"+)4jK'QF0$\"+**QDkWF07%7$$
\"+WH>YYF0$\"+?FHb_F07$$\"+o7\\F[F0$\"+#\\\"R=UF07$$\"+$o^y\"\\F0$\"+%
[\\bY%F07%7$$\"+Cq7'p&F0$\"+MQ\"[D&F07$$\"+Y.#G)eF0$\"+y.()=UF07$$\"+)
)H*=(fF0$\"+\"Q&\\mWF07%7$$\"+a,tYnF0$\"+sTWa_F07$$\"+u.[PpF0$\"+S+C>U
F07$$\"+cAeDqF0$\"+(37sY%F07%7$$\"+-9z(z(F0$\"+`B:a_F07$$\"+%G#o\"*zF0
$\"+f=`>UF07$$\"+Q7.z!)F0$\"+F,xnWF07%7$$\"+Sq<\\))F0$\"+1t\"RD&F07$$
\"+/)fb/*F0$\"+1pw>UF07$$\"+)[5B8*F0$\"+\")[@oWF07%7$$\"+A')z+**F0$\"+
)[CPD&F07$$\"+Q,#*45F*$\"+C(f*>UF07$$\"+_ma=5F*$\"+0ndoWF07%7$Fc_l$\"+
'*y:j_F07$Fa]\\l$\"+u%*y:jF07$F4$\"+R5*y3'F07%7$$!+kESZ*)F0Fj`]l7$$!+y
TLZ*)F0F]a]l7$$!+`z#*y!*F0$\"+8m*y3'F07%7$$!+8]$[*yF0$\"+0z:j_F07$$!+r
'QY*yF0$\"+l%*y:jF07$$!+E,EE!)F0$\"+!f7z3'F07%7$$!+@qQUoF0$\"+rz:j_F07
$$!+0N#=%oF0$\"+*R*y:jF07$$!+QW_tpF0$\"+\\%ez3'F07%7$$!+#y%G!z&F0$\"+@
&eJE&F07$$!+'ei')y&F0$\"+\\))y:jF07$$!+$f#f?fF0$\"+s/4)3'F07%7$$!+Ch>R
ZF0$\"+gJ;j_F07$$!+'3)[MZF0$\"+5Uy:jF07$$!+Q]3n[F0$\"+sNZ)3'F07%7$$!+m
$*=\"p$F0$\"+mT?j_F07$$!+'oJsn$F0$\"+/Ku:jF07$$!+#*4#=\"QF0$\"+Glg*3'F
07%7$$!+vsI`EF0$\"+,mgj_F07$$!+>1&)4EF0$\"+p2M:jF07$$!+Kgs]FF0$\"+Cd1$
4'F07%7$$!+&[8yk\"F0$\"+hFon_F07$$!+^735:F0$\"+4YE6jF07$$!+&))[.n\"F0$
\"+S!RD5'F07%7$$!+ONMreFdt$\"+eOom_F07$$!+WA(\\l%Fdt$\"+7PE7jF07$$!+A%
*HDiFdt$\"+JO4,hF07%7$$\"+]rjE\\Fdt$\"+LDr9jF07$$\"+]'y'*f&Fdt$\"+P[Bk
_F07$$\"+7!eqw'Fdt$\"+\\H3+bF07%7$$\"+>L5@:F0$\"+!=,EJ'F07$$\"+>9zO;F0
$\"+!>YjE&F07$$\"+%3EDu\"F0$\"+`!Gt]&F07%7$$\"+fE.lDF0$\"+Pbc6jF07$$\"
+P_7)p#F0$\"+L=Qn_F07$$\"+7G$)*z#F0$\"+4345bF07%7$$\"+!*=)Gh$F0$\"+*oL
4J'F07$$\"+k\"Rbv$F0$\"+\"o8!o_F07$$\"+fz,bQF0$\"+XYk6bF07%7$$\"+V*[Bm
%F0$\"+N5\\5jF07$$\"+p_L6[F0$\"+NjXo_F07$$\"+@JL4\\F0$\"+cno7bF07%7$$
\"+&)Rr7dF0$\"+S>;5jF07$$\"+&QLi'eF0$\"+Iayo_F07$$\"+Cv;jfF0$\"+$)*RM^
&F07%7$$\"+S&\\Ow'F0$\"+*34*4jF07$$\"+))4c?pF0$\"+\"GQ!p_F07$$\"+9vp;q
F0$\"+_t+9bF07%7$$\"+H7(\\\"yF0$\"+O*4(4jF07$$\"+dC]uzF0$\"+MuBp_F07$$
\"+'*>-q!)F0$\"+UxW9bF07%7$$\"+4Xcm))F0$\"+y'\\&4jF07$$\"+NB<G!*F0$\"+
#p(Rp_F07$$\"+7A?B\"*F0$\"+\"=)z9bF07%7$$\"+\\YN=**F0$\"+Y#=%4jF07$$\"
+NX;35F*$\"+C\"H&p_F07$$\"+-yi<5F*$\"+hI3:bF07%7$Fc_lF]a]l7$Fa]\\l$\"+
a5UotF07$F4$\"+>E_SrF07%7$$!+mESZ*)F0$\"+w%*y:jF07$$!+wTLZ*)F0$\"+_5Uo
tF07$$!+_z#*y!*F0$\"+#>G09(F07%7$$!+I]$[*yF0$\"+%[*y:jF07$$!+a'QY*yF0$
\"+W5UotF07$$!+;,EE!)F0$\"+tTaSrF07%7$$!+crQUoF0$\"+]&*y:jF07$$!+qL#=%
oF0$\"+y4UotF07$$!+iV_tpF0$\"+i+fSrF07%7$$!+seG!z&F0$\"+,,z:jF07$$!+'
\\h')y&F0$\"+F/UotF07$$!+u>f?fF0$\"+BBsSrF07%7$$!++\\?RZF0$\"+yZz:jF07
$$!+5$zWt%F0$\"+]dTotF07$$!+_+3n[F0$\"+Bt5TrF07%7$$!+e5E\"p$F0$\"+,n$e
J'F07$$!+%**frn$F0$\"+FQPotF07$$!+/,y6QF0$\"+)[bA9(F07%7$$!+s$3Rl#F0$
\"+hLE;jF07$$!+A&\\#4EF0$\"+nr%zO(F07$$!+A*y.v#F0$\"++L$e9(F07%7$$!+D9
W^;F0$\"+,g!3K'F07$$!+6LX1:F0$\"+FXSjtF07$$!+u*o\"o;F0$\"+R))zbrF07%7$
$!+@)f;\"eFdt$\"+%Rb'=jF07$$!+ffl9ZFdt$\"+M^bltF07$$!+Q*)ygiFdt$\"+Ssg
_rF07%7$$\"+9Z^\")\\Fdt$\"+YpmntF07$$\"+'3,[a&Fdt$\"+#eVlJ'F07$$\"+8-v
OnFdt$\"+X&f6b'F07%7$$\"+\\oDI:F0$\"+')R;mtF07$$\"+*)yjF;F0$\"+Ul/=jF0
7$$\"+c*ovt\"F0$\"+bK9dlF07%7$$\"+&H*HvDF0$\"+tLSltF07$$\"+,'eyo#F0$\"
+br!)=jF07$$\"+CLJ%z#F0$\"+'zr%flF07%7$$\"+U0wBOF0$\"+Q!Q\\O(F07$$\"+7
0mWPF0$\"+!\\s#>jF07$$\"+%4$>\\QF0$\"+=#y2c'F07%7$$\"+eLltYF0$\"+3Thkt
F07$$\"+a3.+[F0$\"+?kf>jF07$$\"+MlH.\\F0$\"+ulkhlF07%7$$\"+')\\LCdF0$
\"+,YPktF07$$\"+%Q7Y&eF0$\"+Ff$)>jF07$$\"+MQ(p&fF0$\"+e)pAc'F07%7$$\"+
9C^vnF0$\"+z6>ktF07$$\"+9\")p3pF0$\"+\\$>+K'F07$$\"+VSQ5qF0$\"+%RPFc'F
07%7$$\"+&zAq#yF0$\"+Xp/ktF07$$\"+\"*3XizF0$\"+$ej,K'F07$$\"+o_hj!)F0$
\"+s%*4jlF07%7$$\"+ziwy))F0$\"+f4$RO(F07$$\"+l0(f,*F0$\"+p&z-K'F07$$\"
+!R@n6*F0$\"+fsQjlF07%7$$\"+:$y1$**F0$\"+fe$QO(F07$$\"+o@$p+\"F*$\"+pY
P?jF07$$\"+;P(p,\"F*$\"+l5ijlF07%7$Fc_lFad^l7$Fa]\\l$\"+KE0@%)F07$F4$
\"+(>aJ>)F07%7$$!+oESZ*)F0$\"+b5UotF07$$!+uTLZ*)F0$\"+JE0@%)F07$$!+]z#
*y!*F0$\"+r(fJ>)F07%7$$!+Z]$[*yF0$\"+j5UotF07$$!+P'QY*yF0$\"+BE0@%)F07
$$!+1,EE!)F0$\"+cd<$>)F07%7$$!+#H(QUoF0$\"+H6UotF07$$!+MK#=%oF0$\"+dD0
@%)F07$$!+&GCN(pF0$\"+v;A$>)F07%7$$!+lpG!z&F0$\"+#o@%otF07$$!+./m)y&F0
$\"+/?0@%)F07$$!+a8f?fF0$\"+uTN$>)F07%7$$!+TP@RZF0$\"+(RE%otF07$$!+p/Z
MZF0$\"+*GZ5U)F07$$!+H]2n[F0$\"+!4TP>)F07%7$$!+PUL\"p$F0$\"+m#p%otF07$
$!+:o3xOF0$\"+?W+@%)F07$$!+n$Q<\"QF0$\"+-[!\\>)F07%7$$!+TOaaEF0$\"+,B#
*otF07$$!+`Uh3EF0$\"+&Q^0U)F07$$!+$*=,]FF0$\"+$=3')>)F07%7$$!+F&oal\"F
0$\"+yM,utF07$$!+4iU-:F0$\"+3-Y:%)F07$$!+%oTdm\"F0$\"+n164#)F07%7$$!+$
o%fidFdt$\"+lgzqtF07$$!+(4@Pw%Fdt$\"+@wn=%)F07$$!+=b$)*G'Fdt$\"+H0H/#)
F07%7$$\"+k*>5-&Fdt$\"+X`\\?%)F07$$\"+OeH0bFdt$\"+T$y*otF07$$\"+*GV[r'
Fdt$\"+**=p-wF07%7$$\"+Ss\"p`\"F0$\"+V<P>%)F07$$\"+)\\x4i\"F0$\"+V>5qt
F07$$\"+Vm$Rt\"F0$\"+^Iy2wF07%7$$\"+OM$Ge#F0$\"+_/z=%)F07$$\"+gWK!o#F0
$\"+MKoqtF07$$\"+O/B!z#F0$\"+\"[\"z4wF07%7$$\"+EXxJOF0$\"+hSV=%)F07$$
\"+GlkOPF0$\"+D'R5P(F07$$\"+y`'[%QF0$\"+th\"4h(F07%7$$\"+k`*>o%F0$\"+v
q==%)F07$$\"+[))o\"z%F0$\"+6mGrtF07$$\"+q?!))*[F0$\"+'*)e;h(F07%7$$\"+
;z\"Ht&F0$\"+$=0!=%)F07$$\"+a%Hg%eF0$\"+.&o9P(F07$$\"+trN_fF0$\"+$G*=7
wF07%7$$\"+7#yUy'F0$\"+<i'yT)F07$$\"+;B$***oF0$\"+pugrtF07$$\"+7[n0qF0
$\"+'*ee7wF07%7$$\"+C3$f$yF0$\"+uqv<%)F07$$\"+iGa`zF0$\"+7mrrtF07$$\"+
nT$)e!)F0$\"+?D*Gh(F07%7$$\"+'R(y()))F0$\"+b$pwT)F07$$\"+[%\\p+*F0$\"+
JV!=P(F07$$\"+NK)=6*F0$\"+2g88wF07%7$$\"+!=\"zR**F0$\"+Wuf<%)F07$$\"+#
)3-15F*$\"+Ui(=P(F07$$\"+z_[;5F*$\"+HPL8wF07%7$Fc_l$\"+LE0@%)F07$$!+]!
))*****F0$\"+6Uot%*F07$F4$\"+wdyX#*F07%7$$!+qESZ*)F0$\"+ME0@%)F07$$!+s
TLZ*)F0$\"+5Uot%*F07$$!+\\z#*y!*F0$\"+^8zX#*F07%7$$!+k]$[*yF0$\"+UE0@%
)F07$$!+?'QY*yF0$\"+-Uot%*F07$$!+'4gi-)F0$\"+Rt!eC*F07%7$$!+GuQUoF0$\"
+3F0@%)F07$$!+)4B=%oF0$\"+OTot%*F07$$!+2U_tpF0$\"+)G`eC*F07%7$$!+g!)G!
z&F0$\"+iK0@%)F07$$!+3$f')y&F0$\"+#e$ot%*F07$$!+L2f?fF0$\"+Fg)fC*F07%7
$$!+\\EARZF0$\"+;!e5U)F07$$!+h:YMZF0$\"+G)yOZ*F07$$!+o*pq'[F0$\"+t[PY#
*F07%7$$!+_*39p$F0$\"+h=5@%)F07$$!++@,xOF0$\"+$)\\jt%*F07$$!+]dp6QF0$
\"+%[avC*F07%7$$!+xg@bEF0$\"+zOe@%)F07$$!+<=%zg#F0$\"+lJ:t%*F07$$!+!=B
'\\FF0$\"+v4R^#*F07%7$$!+NO'*f;F0$\"+naKF%)F07$$!+,6$z\\\"F0$\"+x8Tn%*
F07$$!+7H-j;F0$\"+R-[i#*F07%7$$!+ufb@dFdt$\"+cE0B%)F07$$!+1)fZ![Fdt$\"
+)=%or%*F07$$!+89/9jFdt$\"+a(3hD*F07%7$$\"+rQ\"30&Fdt$\"+#obKZ*F07$$\"
+H>]vaFdt$\"+i6[@%)F07$$\"+<CF)p'Fdt$\"+Ec]a')F07%7$$\"+@(y>a\"F0$\"+f
UQs%*F07$$\"+<g\"fh\"F0$\"+&e_BU)F07$$\"+#3i6t\"F0$\"+tK$*e')F07%7$$\"
+UXf)e#F0$\"+**f#>Z*F07$$\"+aLcuEF0$\"+X3\"GU)F07$$\"+a**3(y#F0$\"+Sqp
g')F07%7$$\"+8(>zj$F0$\"+iXkr%*F07$$\"+T8]IPF0$\"+#G#4B%)F07$$\"+me_TQ
F0$\"+8Koh')F07%7$$\"+1+S)o%F0$\"+l,Xr%*F07$$\"+1UG&y%F0$\"+zmGB%)F07$
$\"+(fG`*[F0$\"+c7Li')F07%7$$\"+k9^RdF0$\"+KuIr%*F07$$\"+1fVReF0$\"+7%
HMU)F07$$\"+#Q'y[fF0$\"+9Azi')F07%7$$\"+iW,\"z'F0$\"+&e)>r%*F07$$\"+mg
>$*oF0$\"+f#QNU)F07$$\"+S1.-qF0$\"+ug8j')F07%7$$\"+8yxUyF0$\"+yJ6r%*F0
7$$\"+tepYzF0$\"+mOiB%)F07$$\"+UJ8b!)F0$\"+c:Sj')F07%7$$\"+aBs%*))F0$
\"+kX/r%*F07$$\"+!\\9++*F0$\"+!G#pB%)F07$$\"+4r83\"*F0$\"+=Ahj')F07%7$
$\"+([(zY**F0$\"+D$))4Z*F07$$\"+^-K05F*$\"+>&[PU)F07$$\"+7q5;5F*$\"+;K
yj')F07%7$Fc_lFe[al7$Fc[al$F\\_wF*7$F4$\"+O<%)H5F*7%7$$!+sESZ*)F0$\"+7
Uot%*F07$$!+qTLZ*)F0F]_bl7$$!+[z#*y!*F0$\"+$HU)H5F*7%7$$!+\"3N[*yF0$\"
+?Uot%*F07$$!+.'QY*yF0$Fj_wF*7$$!+(3gi-)F0$\"+#*Q%)H5F*7%7$$!+kvQUoF0$
\"+'G%ot%*F07$$!+iH#=%oF0$\"+r:j_5F*7$$!+IT_tpF0$\"+!\\[)H5F*7%7$$!+f
\"*G!z&F0$\"+U[ot%*F07$$!+4#e')y&F0$\"+;:j_5F*7$$!+5,f?fF0$\"+)yh)H5F*
7%7$$!+C;BRZF0$\"+N'*ot%*F07$$!+'e_Wt%F0$\"+P5j_5F*7$$!+p[1n[F0$\"+o3!
*H5F*7%7$$!+]_[\"p$F0$\"+)[MPZ*F07$$!+-e$pn$F0$\"+^li_5F*7$$!+GAl6QF0$
\"+a/-I5F*7%7$$!+P!Hfl#F0$\"+$zZUZ*F07$$!+d)Gsg#F0$\"+@_d_5F*7$$!+23@
\\FF0$\"+N#=/.\"F*7%7$$!+W@,l;F0$\"+z'o2[*F07$$!+#f#)G\\\"F0$\"+KJ#>0
\"F*7$$!+jv&*f;F0$\"+w8fJ5F*7%7$$!+:\"Hno&Fdt$\"+*R\"Rv%*F07$$!+lmeR[F
dt$\"+g3Y_5F*7$$!+*))>XL'Fdt$\"+pN!3.\"F*7%7$$\"+EL3u]Fdt$\"+1wf_5F*7$
$\"+uCB_aFdt$\"+QR-u%*F07$$\"+Q4I&o'Fdt$\"+=^]1(*F07%7$$\"+?V&fa\"F0$
\"+m!GD0\"F*7$$\"+=/%>h\"F0$\"+V$>ZZ*F07$$\"+tT(*G<F0$\"+-3U5(*F07%7$$
\"+u59$f#F0$\"+K5\\_5F*7$$\"+Ao,qEF0$\"+%o*3v%*F07$$\"+8.g%y#F0$\"+()>
*>r*F07%7$$\"+m'zFk$F0$\"+d#oC0\"F*7$$\"+)QTcs$F0$\"+NuJv%*F07$$\"+S>(
)QQF0$\"+l$pGr*F07%7$$\"+h)pMp%F0$\"+lDX_5F*7$$\"+^V@!y%F0$\"+\\VZv%*F
07$$\"+J]c#*[F0$\"+zOW8(*F07%7$$\"+ZJtWdF0$\"+r5W_5F*7$$\"+BU@MeF0$\"+
)G*ev%*F07$$\"+!oVf%fF0$\"+A4&Qr*F07%7$$\"+?/N'z'F0$\"+>BV_5F*7$$\"+3,
'y)oF0$\"+8onv%*F07$$\"+w%G\"**pF0$\"+CT:9(*F07%7$$\"+%H-#[yF0$\"+caU_
5F*7$$\"+#Rr7%zF0$\"+Qauv%*F07$$\"+#)\\=_!)F0$\"+gzQ9(*F07%7$$\"+/r@+*
)F0$\"+X*>C0\"F*7$$\"+S(>X**)F0$\"+]0!eZ*F07$$\"+$[_^5*F0$\"++Md9(*F07
%7$$\"+<#\\B&**F0$\"+GaT_5F*7$$\"+y]w/5F*$\"+;d%eZ*F07$$\"+'f0e,\"F*$
\"+uQs9(*F0-%&COLORG6]dl%$HUEG\"\"!FbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
FbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbclFbbcl
-%%VIEWG6$;$!+++++6F*$\"+++++6F*Ffbcl-%+AXESLABELSG6$Q\"t6\"Q%y(t)F_cc
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 12 "with(plots):" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "solut1
 := dsolve(\{de1, y(1)=10\}, y(t));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
39 "solut := dsolve(\{de1, y(1)=100\}, y(t));" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "solut2 := dsolve(\{de1, y(1)=2\}, y(t));" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 64 "plot(\{rhs(solut1), rhs(solut2), rhs(solut)
\}, t=0..6, y=-10..10);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%'solut1G/-%\"yG6#%\"tG*&*&,&*$)F)\"\"#\"\"\"F0*&,&-%$expG6#!\"\"F0\"
#5F6F0F3F6F6F0-F46#,$F)F6F0F0F)F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%&solutG/-%\"yG6#%\"tG*&*&,&*$)F)\"\"#\"\"\"F0*&,&-%$expG6#!\"\"F0\"$+
\"F6F0F3F6F6F0-F46#,$F)F6F0F0F)F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%'solut2G/-%\"yG6#%\"tG*&*&,&*$)F)\"\"#\"\"\"F0*&,&-%$expG6#!\"\"F0F/F
6F0F3F6F6F0-F46#,$F)F6F0F0F)F6" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 
300 {PLOTDATA 2 "6'-%'CURVESG6$7fp7$$\"3s*****\\Smp3%!#?$\"3)od\"=_MH!
Q'!#97$$\"3Y******4G$R<)F*$\"3%))*)e3RTr<$F-7$$\"3'******>#**3E7!#>$\"
3jY?st?Y4@F-7$$\"3*)*****>c'yM;F6$\"3G=)>=\"3lv:F-7$$\"3\"******H?$[V?
F6$\"3s$QFWm'Qb7F-7$$\"3%)*****H%)z@X#F6$\"3^L([y)f*=/\"F-7$$\"3%)****
*R[w3'GF6$\"39Q?evk=%*))!#:7$$\"3')*****\\7t&pKF6$\"3EZl2xdu]xFM7$$\"3
9+++l(p#yOF6$\"3SU'otIE:'oFM7$$\"3#)*****fSmp3%F6$\"3ukTCy6E]hFM7$$\"3
;+++ZIm&\\%F6$\"3aaCwApTobFM7$$\"3v*****pofV!\\F6$\"3w(HKy*yj$3&FM7$$
\"36+++Gj08`F6$\"3sR/nTS_tYFM7$$\"3x******oHv@dF6$\"3!fua[Jv?K%FM7$$\"
30+++4'\\/8'F6$\"3>-<_c$ev,%FM7$$\"3s******\\i9RlF6$\"3g,'\\b9t6v$FM7$
$\"33+++\"*G%y%pF6$\"3Sn\"ptD!>;NFM7$$\"3O+++J&RlN(F6$\"3o'*QH'pvtI$FM
7$$\"3M*****><O_w(F6$\"3i(zK.O(f?JFM7$$\"3q*****H\"G$R<)F6$\"3)G(pVq&
\\D&HFM7$$\"3'******HXHEe)F6$\"3TIjv,jb+GFM7$$\"3K+++%4E8**)F6$\"3%=kd
%z!GCm#FM7$$\"3o+++NF-+%*F6$\"3s9B'*3iNODFM7$$\"3e*****\\P>(3)*F6$\"3'
f*zqXM$3U#FM7$$\"3.+++-;u@5!#=$\"3RIYS.Pf9BFM7$$\"31+++m7hi5F`s$\"3Zcl
2$oll@#FM7$$\"3%*******H4[.6F`s$\"3<E@+%zOe7#FM7$$\"3(******Rf]V9\"F`s
$\"3T^>a<[iT?FM7$$\"3.+++A**3E7F`s$\"3mtoz5U9!*=FM7$$\"3%*******\\#HyI
\"F`s$\"3-bLZ'*Qsd<FM7$$\"3'******>?]*y8F`s$\"3M(\\$*zpt`l\"FM7$$\"31+
++b62]9F`s$\"3;;%H)ot9j:FM7$$\"3))*****z5#>@:F`s$\"3QYkm*GC'z9FM7$$\"3
))******fIJ#f\"F`s$\"3!QB%*\\lPOS\"FM7$$\"3#******R'\\bM<F`s$\"3C(*\\p
]Lcq7FM7$$\"3/+++pozw=F`s$\"3m$e(p/)4z:\"FM7$$\"3()*****RxQ!>?F`s$\"3'
G)Q-ntNh5FM7$$\"3!******zn!Gh@F`s$\"3)=.Y%RhBx(*!#;7$$\"3,+++$eANI#F`s
$\"3-AF%eGAh/*Fdw7$$\"37+++)[kdW#F`s$\"3lD()R#4W=S)Fdw7$$\"3)******\\G
'plFF`s$\"3MrHngyb+sFdw7$$\"3%)*****>3Gc3$F`s$\"3M$4:W!G@biFdw7$$\"3B+
++z)fbS$F`s$\"3O!)RJ:vX$\\&Fdw7$$\"3++++v;\\DPF`s$\"3IaN.)4,y'[Fdw7$$
\"3A++++nfpVF`s$\"3!)yEK;K2**QFdw7$$\"3W+++D<q8]F`s$\"3#oNji\\([$>$Fdw
7$$\"3s*****z8*y&H'F`s$\"3IvjMl8T\\AFdw7$$\"3i*****zG[W[(F`s$\"3aB!yx8
f/p\"Fdw7$$\"3m*****z)fB:()F`s$\"3M1B'>TzJH\"Fdw7$$\"3=+++)Q=\"))**F`s
$\"3nl8>!G#H-5Fdw7$$\"3*******R'=pD6!#<$\"3X)*e:?j<6zFd[l7$$\"33+++lN?
c7Fd[l$\"3A5.*zj=BH'Fd[l7$$\"3)******>Me6P\"Fd[l$\"3%QW9UXuY>&Fd[l7$$
\"36+++&>q0]\"Fd[l$\"3&pX2zi;dA%Fd[l7$$\"3'******\\U80j\"Fd[l$\"3m7&p'
G!GRY$Fd[l7$$\"35+++0ytb<Fd[l$\"3W)p#=W1(*zGFd[l7$$\"3++++RNXp=Fd[l$\"
3%=rU&p(e![CFd[l7$$\"3.+++XDn/?Fd[l$\"3#3'=\"HD)RH?Fd[l7$$\"3.+++!y?#>
@Fd[l$\"33Y_K`)4(Q<Fd[l7$$\"3)*******3wY_AFd[l$\"3??+h=1(*e9Fd[l7$$\"3
#)******HOTqBFd[l$\"3mdJd_qi`7Fd[l7$$\"39+++4\">)*\\#Fd[l$\"3As$fU:R^1
\"Fd[l7$$\"38+++EP/BEFd[l$\"3[G%e@bJ)[\"*F`s7$$\"3y*****zo:;v#Fd[l$\"3
>O`#4f-%HyF`s7$$\"3A+++%)[opGFd[l$\"37'Qp`#pR-oF`s7$$\"3!******>YQq*HF
d[l$\"3Sj<#QYw*eeF`s7$$\"3(*******QIKHJFd[l$\"3:HSv)*3JH]F`s7$$\"3*)**
***4:xWC$Fd[l$\"3O<T)Hq\"Q6WF`s7$$\"3;+++[n%)oLFd[l$\"3S)ps)RAtNQF`s7$
$\"3y******4FL(\\$Fd[l$\"3=7J#Q.#pDLF`s7$$\"3()*****z:JIi$Fd[l$\"3'=^
\\ftsq*GF`s7$$\"3++++p3lWPFd[l$\"33`'o2'\\dQDF`s7$$\"3')*****>#))ozQFd
[l$\"3gR3$\\3Jb>#F`s7$$\"3e******Hk-,SFd[l$\"3GAS%o<7%H>F`s7$$\"36+++D
-eITFd[l$\"3e4TG:qz#o\"F`s7$$\"3w******=_(zC%Fd[l$\"3g-pU&\\T\")[\"F`s
7$$\"3M+++b*=jP%Fd[l$\"3))eZ#)4pI-8F`s7$$\"3i******3/3(\\%Fd[l$\"3Wtk3
e#=(\\6F`s7$$\"35+++C4JBYFd[l$\"3r&oNBig,,\"F`s7$$\"3u*****\\KCnu%Fd[l
$\"3KOh-&*z53*)F67$$\"3u******=n#f([Fd[l$\"3f'y[!pKZ:yF67$$\"3P+++!)RO
+]Fd[l$\"3moD/>2#[*oF67$$\"3,+++_!>w7&Fd[l$\"3#3]'peTNpgF67$$\"3Q+++*Q
?QD&Fd[l$\"3y`Ukn(3;N&F67$$\"3G+++5jyp`Fd[l$\"3]nf\">1?&pZF67$$\"38+++
Ujp-bFd[l$\"3KVsShR4#=%F67$$\"3++++gEd@cFd[l$\"3`Ok$)\\A'*>PF67$$\"3;+
++4'>$[dFd[l$\"3WR8@HGz%G$F67$$\"35+++6EjpeFd[l$\"38Fo!*=2?<HF67$$\"\"
'\"\"!$\"37(GOi$*H*oDF6-%'COLOURG6&%$RGBG$\"#5!\"\"$FhglFhglFbhl-F$6$7
fp7$F($\"3OJk(*eQg*f'!#87$F/$\"33n&*=zQM'G$Fihl7$F4$\"31Hx3Y2'>=#Fihl7
$F:$\"3!oL&G7nzH;Fihl7$F?$\"3S0)>^A?&)H\"Fihl7$FD$\"3iv@!pV(ox5Fihl7$F
I$\"356m!Qo_'*>*F-7$FO$\"3gj'3I\"=(o,)F-7$FT$\"3Qg[6*)40(4(F-7$FY$\"3W
=:%zu,8O'F-7$Fhn$\"3!\\XIlMA%fdF-7$F]o$\"3)*oeBd\\%zD&F-7$Fbo$\"31B^wV
&*pL[F-7$Fgo$\"3So?c%3O,Z%F-7$F\\p$\"3/i@6)*y6bTF-7$Fap$\"3i9UNsCazQF-
7$Ffp$\"3QLr#e1\\kj$F-7$F[q$\"3*\\_m$pPU?MF-7$F`q$\"3G)zhOW#>FKF-7$Feq
$\"3WMxbzdL`IF-7$Fjq$\"39:Pkld3'*GF-7$F_r$\"3/YJ0lw<`FF-7$Fdr$\"3@X\\+
51uAEF-7$Fir$\"3x)3#pWb@.DF-7$F^s$\"3'ya(3hGH$R#F-7$Fds$\"33,t/MW'=H#F
-7$Fis$\"3!f@x?I')z>#F-7$F^t$\"3vwS9d$\\36#F-7$Fct$\"3Y93[/?5a>F-7$Fht
$\"3)\\KiN:rq\"=F-7$F]u$\"3lgc@1D:6<F-7$Fbu$\"3c-(='*[1dh\"F-7$Fgu$\"3
`'e#>WOEH:F-7$F\\v$\"3C'pe([qh]9F-7$Fav$\"3\"onVxmuGJ\"F-7$Ffv$\"3I)\\
u])yD'>\"F-7$F[w$\"3%)eK=0&)H'4\"F-7$F`w$\"3sT'=1l/(45F-7$Ffw$\"33Q^fL
d(*R$*FM7$F[x$\"3S`5xb?vs')FM7$F`x$\"3mttY_&p%GuFM7$Fex$\"3I$[$Q\"*30
\\kFM7$Fjx$\"3kN:H&\\^'fcFM7$F_y$\"3i$yEH6U6,&FM7$Fdy$\"3p=`e>Ps1SFM7$
Fiy$\"3yaj\\vV)[F$FM7$F^z$\"33d#)p\"Q)Q&H#FM7$Fcz$\"3Q7$G?;\"[:<FM7$Fh
z$\"3m>rjoic.8FM7$F][l$\"3\"f\\&f)4rB+\"FM7$Fb[l$\"3n')4>`Q(=%yFdw7$Fh
[l$\"3i/9Ks'*RuhFdw7$F]\\l$\"3+EX8ah0[]Fdw7$Fb\\l$\"3%G6p*=\"*HeSFdw7$
Fg\\l$\"3+@#)Q'y[YG$Fdw7$F\\]l$\"3+58r*4=bp#Fdw7$Fa]l$\"3'fY'>2@%GE#Fd
w7$Ff]l$\"3E#G_mbRo%=Fdw7$F[^l$\"3s-sQ>0hg:Fdw7$F`^l$\"3))*eQGURyG\"Fd
w7$Fe^l$\"3-e>7u%e(*3\"Fdw7$Fj^l$\"3!))\\G]Xf)*4*Fd[l7$F__l$\"3y\"f8_z
0Wo(Fd[l7$Fd_l$\"3[+hU'GsvX'Fd[l7$Fi_l$\"31u,p6+W:bFd[l7$F^`l$\"3ujn&*
[=-iYFd[l7$Fc`l$\"3$Rp&)GdJI#RFd[l7$Fh`l$\"3#*=B8Ci/\"Q$Fd[l7$F]al$\"3
7%)*en_FQ)GFd[l7$Fbal$\"3)G\"3UDzd]CFd[l7$Fgal$\"3W/>g@`t#4#Fd[l7$F\\b
l$\"3Khq2u&e&)z\"Fd[l7$Fabl$\"3tW'G'Qy:A:Fd[l7$Ffbl$\"3(3\"oAWRr68Fd[l
7$F[cl$\"3>m-8<9G?6Fd[l7$F`cl$\"3Mgn;GUr>(*F`s7$Fecl$\"3k,Dgqd1I$)F`s7
$Fjcl$\"3oq>D=fy5sF`s7$F_dl$\"3B@YqV_f1iF`s7$Fddl$\"3W-#Rb?5XO&F`s7$Fi
dl$\"3jz1&zpS)3YF`s7$F^el$\"3c%Rl`Ud[)RF`s7$Fcel$\"350%*[pB`OMF`s7$Fhe
l$\"3!fLG?gi$pHF`s7$F]fl$\"3#>7y)*=4yf#F`s7$Fbfl$\"3<laaS>EIAF`s7$Fgfl
$\"3I?\")))Rf#p%>F`s7$F\\gl$\"3IS;\"QlJ`o\"F`s7$Fagl$\"3OlB8y:so9F`s7$
Ffgl$\"3e[k[V]en7F`s-F\\hl6&F^hlFbhlF_hlFbhl-F$6$7fp7$F($\"3Eo'=m5;63
\"F-7$F/$\"3++jb'*Rf$Q&FM7$F4$\"3)[e$>/:\\uNFM7$F:$\"3;1GhIZ+qEFM7$F?$
\"33(ox/!ROF@FM7$FD$\"3c#4*)=wXcw\"FM7$FI$\"3'[c%pw<J2:FM7$FO$\"3#e?J!
zEf88FM7$FT$\"3KD/\")))*\\H;\"FM7$FY$\"3hu+9=1YU5FM7$Fhn$\"3[CgZcy+R%*
Fdw7$F]o$\"3b&Hx?rzyh)Fdw7$Fbo$\"3(yD*\\UeEBzFdw7$Fgo$\"3$etx*)*[0GtFd
w7$F\\p$\"3nA$RABlB\"oFdw7$Fap$\"3#*Q:R3cGhjFdw7$Ffp$\"3G/`WGLTjfFdw7$
F[q$\"3'*4A%>jz)4cFdw7$F`q$\"3GgA&)oGo$H&Fdw7$Feq$\"3azrYE<A4]Fdw7$Fjq
$\"3snDS8='>v%Fdw7$F_r$\"3DPT%e<$>=XFdw7$Fdr$\"3JnMKv5&[I%Fdw7$Fir$\"3
mZH6n:Q4TFdw7$F^s$\"3akm^Q$R'HRFdw7$Fds$\"3y_?IN\"4Qw$Fdw7$Fis$\"3l)yO
tiW.h$Fdw7$F^t$\"3IAh<%R?zY$Fdw7$Fct$\"3eA(e**pu<@$Fdw7$Fht$\"3![`A)=m
\"z)HFdw7$F]u$\"3nUbMnd$\\\"GFdw7$Fbu$\"3wt^'Gb-\"fEFdw7$Fgu$\"3\\pQVs
)4!=DFdw7$F\\v$\"3e+)[()p!o*Q#Fdw7$Fav$\"3;L<S0h-l@Fdw7$Ffv$\"39#fAQyZ
\\(>Fdw7$F[w$\"3kdxHRo77=Fdw7$F`w$\"3'z>UjMr6n\"Fdw7$Ffw$\"3MJ(*\\#R@!
[:Fdw7$F[x$\"3nll#*R<cR9Fdw7$F`x$\"3u!o];SBvB\"Fdw7$Fex$\"3cPL8R?uy5Fd
w7$Fjx$\"3!)\\_g3_j4&*Fd[l7$F_y$\"3oP1YT)f9Y)Fd[l7$Fdy$\"3A*y5.2`7%oFd
[l7$Fiy$\"31)GAr<ZMm&Fd[l7$F^z$\"3+]#)*39Q,4%Fd[l7$Fcz$\"3!4:?AG+&eJFd
[l7$Fhz$\"3i#QP!47.%\\#Fd[l7$F][l$\"3N;gM_R)Q+#Fd[l7$Fb[l$\"3]y)))oXPQ
k\"Fd[l7$Fh[l$\"3cB/(fe!Gj8Fd[l7$F]\\l$\"3M0<poAEp6Fd[l7$Fb\\l$\"3/:C#
3*))eR**F`s7$Fg\\l$\"3a?;1A$\\9_)F`s7$F\\]l$\"3w.WWh%>&*R(F`s7$Fa]l$\"
3af?0ry[UlF`s7$Ff]l$\"3UJbds/a\"o&F`s7$F[^l$\"3Gw3@(*[_g]F`s7$F`^l$\"3
Uw\\&=U2\"RWF`s7$Fe^l$\"3C+#z8pjQ'RF`s7$Fj^l$\"3&o05>%zT4NF`s7$F__l$\"
3d_EQ%4y98$F`s7$Fd_l$\"39*\\&HL_G&y#F`s7$Fi_l$\"3<m?7'3TW]#F`s7$F^`l$
\"3CI@U]\\vNAF`s7$Fc`l$\"3cfE_!e@#*)>F`s7$Fh`l$\"3y*>w&*4I\")z\"F`s7$F
]al$\"3N'GU2(RG8;F`s7$Fbal$\"3eKLB9w,V9F`s7$Fgal$\"3'*36sP6Q%H\"F`s7$F
\\bl$\"3/!fzeL2b;\"F`s7$Fabl$\"3&*H#*p8-mP5F`s7$Ffbl$\"3kwaG5`Z\\$*F67
$F[cl$\"3)HgC3oKdO)F67$F`cl$\"3G?e099YkvF67$Fecl$\"3m:=6LB<wnF67$Fjcl$
\"3,])RH)oc4hF67$F_dl$\"3OqWeEKb#[&F67$Fddl$\"3k!Rr2I'[J\\F67$Fidl$\"3
%f23qrMMT%F67$F^el$\"31oEj#=)flRF67$Fcel$\"3!=0!fmo:aNF67$Fhel$\"37,Iu
+R(y=$F67$F]fl$\"3]MoTwOJ%)GF67$Fbfl$\"3OHIg)e!QrDF67$Fgfl$\"3@-pZDZ-?
BF67$F\\gl$\"3CBU'G$=qy?F67$Fagl$\"3%)3J!y:x4(=F67$Ffgl$\"3_\"*[-.q`q;
F6-F\\hl6&F^hlF_hlF_hlFbhl-%+AXESLABELSG6$Q\"t6\"Q\"yF^[o-%%VIEWG6$;Fb
hlFfgl;$!#5Fhgl$F`hlFhgl" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 195 "We can see from the pl
ots of the solution that as t approaches 0, the function goes towards \+
infinity.  Plotting for a0 = 2, 10, and 100, we see that increasing a0
 shifts the graph to the right.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 258 "" 0 "" {TEXT -1 127 "B.  Let a0 be the value of a fo
r which the transition from one type of behaviour to another occurs.  \+
Estimate the value of a0. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 122 "Observing the direction field of the differentia
l equation, a0 appears to be zero.  The behavior appears to change at \+
y=0." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 258 "" 0 "" 
{TEXT -1 76 "C.  Solve the initial value problem and find the critical
 value a0 exactly. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "unas
sign('a', 't');" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "solution := dsol
ve(\{de1, y(1)=a\}, y(t));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "deriv
1solution := diff(solution, t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "
deriv2solution := diff(deriv1solution, t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%)solutionG/-%\"yG6#%\"tG*&*&,&*$)F)\"\"#\"\"\"F0*&,&-
%$expG6#!\"\"F6%\"aGF0F0F3F6F0F0-F46#,$F)F6F0F0F)F6" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%/deriv1solutionG/-%%diffG6$-%\"yG6#%\"tGF,,(-%$expG
6#,$F,!\"\"\"\"#*&*&,&*$)F,F3\"\"\"F9*&,&-F/6#F2F2%\"aGF9F9F<F2F9F9F.F
9F9F,F2F2*&*&F6F9F.F9F9*$F8F9F2F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%/deriv2solutionG/-%%diffG6$-%\"yG6#%\"tG-%\"$G6$F,\"\"#,,-%$expG6#,$F
,!\"\"!\"%*&*&,&*$)F,F0\"\"\"F=*&,&-F36#F6F6%\"aGF=F=F@F6F=F=F2F=F=F,F
6F=*&*(F0F=F:F=F2F=F=*$F<F=F6F=*&*&F0F=F2F=F=F,F6F6*&*(F0F=F:F=F2F=F=*
$)F,\"\"$F=F6F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "rhsol1 :
= 0 = rhs(deriv1solution);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "rhsol
2 := 0 = rhs(deriv2solution);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'rh
sol1G/\"\"!,(-%$expG6#,$%\"tG!\"\"\"\"#*&*&,&*$)F,F.\"\"\"F4*&,&-F)6#F
-F-%\"aGF4F4F7F-F4F4F(F4F4F,F-F-*&*&F1F4F(F4F4*$F3F4F-F-" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%'rhsol2G/\"\"!,,-%$expG6#,$%\"tG!\"\"!\"%*&*&,
&*$)F,\"\"#\"\"\"F5*&,&-F)6#F-F-%\"aGF5F5F8F-F5F5F(F5F5F,F-F5*&*(F4F5F
1F5F(F5F5*$F3F5F-F5*&*&F4F5F(F5F5F,F-F-*&*(F4F5F1F5F(F5F5*$)F,\"\"$F5F
-F5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 43 "Evaluate for critical values of critical a:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "avalue1:=solve(subs
(t=1, rhsol2), a);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "avalue2:=solv
e(subs(t=1, rhsol1), a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(avalue1
G,$-%$expG6#!\"\"#\"\"'\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(ava
lue2G-%$expG6#!\"\"" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 82 "D.  Desc
ribe the behavior of the solution corresponding to the inital value of
 a0." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "solutiona1 := dsolv
e(\{de1, y(1)=avalue1\}, y(t));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "
solutiona2 := dsolve(\{de1, y(1)=avalue2\}, y(t));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%+solutiona1G/-%\"yG6#%\"tG*&*&,&*$)F)\"\"#\"\"\"F0#
F0\"\"&F0F0-%$expG6#,$F)!\"\"F0F0F)F7" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%+solutiona2G/-%\"yG6#%\"tG*&F)\"\"\"-%$expG6#,$F)!\"\"F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot(\{rhs(solutiona1), rhs(
solutiona2)\}, t=-4..10, y=-10..4);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 
300 300 {PLOTDATA 2 "6&-%'CURVESG6$7fn7$$!\"%\"\"!$!3WpdK,g#R=#!#:7$$!
3vmmTg*4P#R!#<$!37=LU%f<\\)>F-7$$!3]LL$3#*>u%QF1$!3(f(*oGlhL!=F-7$$!3E
++D\"))H6x$F1$!308^*e-oxj\"F-7$$!3cmmmT)R[p$F1$!3+1Cg78x'[\"F-7$$!3FLe
9'Gg%GOF1$!3eca')e#*Gm8F-7$$!3'***\\iI23iNF1$!3QWeX%Q]^D\"F-7$$!3mmT5v
6q&\\$F1$!3grzWI:l_6F-7$$!3PLLe>;KHMF1$!3M/PL>89e5F-7$$!33+]P9,-!G$F1$
!3l)4izB#3<()!#;7$$!3ymm;4'=28$F1$!3c)pu[HZj;(Ffn7$$!3)pmmmVF/)HF1$!3_
?cCV&>.(eFfn7$$!3vmm;ki8IGF1$!3'*p)p*e)\\kz%Ffn7$$!3')**\\P*Rf0o#F1$!3
C[b\"Qa3=\"RFfn7$$!3+LLeMD)4`#F1$!3+&HC-z$R!=$Ffn7$$!3)om;HtGOD#F1$!3-
du:+k&f9#Ffn7$$!3%)***\\i$\\Wm>F1$!3iSb\"R/q]S\"Ffn7$$!3Mmm\"H/R%p;F1$
!3ew#p)fpOj))F17$$!3+++D^cQt8F1$!3\"3R#)=!Q3BaF17$$!3%HLL$[$e)o5F1$!3F
1tm9Ad7JF17$$!33kmmT`I1!)!#=$!35>*f^))fHy\"F17$$!3#Q*****\\ap')\\F\\r$
!3:5HAp&R2@)F\\r7$$!3q)*****\\noa>F\\r$!3?\"4I`!fmwBF\\r7$$\"3uH+++X:s
'*!#>$\"39Jx:LlY!y)F\\s7$$\"3,NL$3d#e?OF\\r$\"3(p#zfY4!3_#F\\r7$$\"3Gq
mm;FpvnF\\r$\"3#=)GbH^.TMF\\r7$$\"3?tmmm[[[%*F\\r$\"3#=Wu$3&*)Hn$F\\r7
$$\"3?++v`xvb7F1$\"3eCGuT/:xNF\\r7$$\"3cmmmO^'4`\"F1$\"3L\")3!zg()=J$F
\\r7$$\"3u++v`7\"H$=F1$\"3$fxtT+\"pJHF\\r7$$\"35,+Dh`V?@F1$\"30jdOe_3W
DF\\r7$$\"3Rnm;/mV?CF1$\"3q2!HP)=N^@F\\r7$$\"3EnmT&RJfp#F1$\"3pqXe!4,#
>=F\\r7$$\"3?LL$eu*3$*HF1$\"3@1_)Rw/0]\"F\\r7$$\"3_LL3dPv,LF1$\"3<[G$o
_dc@\"F\\r7$$\"3Q++D'oY/d$F1$\"3JVX)ezS[+\"F\\r7$$\"3#RLL3TU1'QF1$\"35
mtU6yPG\")F\\s7$$\"3'********)HWgTF1$\"3Y!)R(Rgf0\\'F\\s7$$\"3w++]n$RP
X%F1$\"3i:`v%)f\">=&F\\s7$$\"37,+v$p=vt%F1$\"3_\"4P]?N-:%F\\s7$$\"3k**
**\\_sg_]F1$\"33>2ww@&*HKF\\s7$$\"3olmmO$GdL&F1$\"3C7D%>m+*pDF\\s7$$\"
3t,++D0-QcF1$\"3Bt!y<a$32?F\\s7$$\"3qKL3x@%>\"fF1$\"3;<D'Q3=.g\"F\\s7$
$\"3*>++]*3T6iF1$\"3C_&yROgiC\"F\\s7$$\"3ImmT?w=$\\'F1$\"3C6QO6I%)G)*!
#?7$$\"3[++v)[Dxy'F1$\"31`v85rO`wF]z7$$\"3'pmm;4!pvqF1$\"355R<!o^=)fF]
z7$$\"3M***\\PMirP(F1$\"3djo3\")yZ8YF]z7$$\"3oNLL`f^nwF1$\"3a]>2w!)p'e
$F]z7$$\"31ML$eXWW'zF1$\"3%yQV\\%)y%oFF]z7$$\"3momTSU\"*e#)F1$\"3r7\"Q
88j&Q@F]z7$$\"3&=+++R,&H&)F1$\"3![]=]SK]o\"F]z7$$\"3lnm;*zC'R))F1$\"3'
*37Jd\"f1G\"F]z7$$\"3#RLLL(G+<\"*F1$\"3bQYsAR*3+\"F]z7$$\"3L++v`du7%*F
1$\"3Yvvu5'*)zo(!#@7$$\"3=,+DE%4ep*F1$\"3oCX_NK)o'fF`]l7$$\"#5F*$\"3Z%
[[i(H**RXF`]l-%'COLOURG6&%$RGBG$Fh]l!\"\"$F*F*Fa^l-F$6$7[p7$F($!3aTBMw
]A6AF-7$F/$!3E[Q-!G.2,#F-7$F5$!3jjafeqsF=F-7$F:$!3%f()*)pV+3m\"F-7$F?$
!3.DZDpDb3:F-7$FD$!399Vl0X/(Q\"F-7$FI$!3kln.tX$\\F\"F-7$FN$!3_Cu4Wm^r6
F-7$FS$!3'3(GRUl8w5F-7$FX$!3cT*H#)*=8z))Ffn7$Fhn$!3&RN,^SyDJ(Ffn7$F]o$
!3bna_t+\\-gFfn7$Fbo$!3\"G(om=j@;\\Ffn7$Fgo$!3%*e'H3q!p?SFfn7$F\\p$!3U
:Ev#)**ozKFfn7$Fap$!3*f:p\"G@YIAFfn7$Ffp$!3]:(G%)eTxZ\"Ffn7$F[q$!3?'G0
]f6%*\\*F17$F`q$!35x>,d[6)*fF17$Feq$!37P6ruDYdOF17$Fjq$!3nZ#=>fd#RBF17
$F`r$!3)*z8$4\"GW\"[\"F17$$!3E'******4\"pqMF\\r$!3M&eJRTBkI\"F17$Fer$!
3GvWSdOt\"[\"F17$$!3[)****\\(*[%*e\"F\\r$!3+.\"e[t&Rh;F17$$!3G)******>
6UA\"F\\r$!3+xnt*RE[)>F17$$!3<)***\\7BfT5F\\r$!3;9aKsx^YAF17$$!3q!)***
*\\Ut*e)F\\s$!3&*H(\\:l.3j#F17$$!3mz***\\PXNw'F\\s$!3O0v=GfJOKF17$$!3h
y*****\\ct$\\F\\s$!3\"\\E1UwUwI%F17$$!3dx***\\in66$F\\s$!3[G.KmJpjmF17
$$!3_w****\\(y\\G\"F\\s$!3ok!*Q>m(yd\"Ffn7$$!3+g(**\\7V)=PF]z$!3QoHc)3
F%)R&Ffn7$$\"3BX-+]757aF]z$\"3KmeHxY,wOFfn7$$\"31D+]iXIa9F\\s$\"3iWue
\"z0oN\"Ffn7$$\"3cD+++!*RnBF\\s$\"3-#=E$=!fNF)F17$$\"3iE++vye$>%F\\s$
\"36\\9)H1NNh%F17$$\"3mF++]nx>gF\\s$\"3q-52QS'\\=$F17$$\"3qG++Dc'f%yF
\\s$\"34qI))GXEHCF17$Fjr$\"3MGF-**R'\\'>F17$$\"3YpT5Sj)))H\"F\\r$\"3)y
Sr&>AHm9F17$$\"3*fL3-Bd0j\"F\\r$\"3IF(**)[=b!=\"F17$$\"3]-DJ?\"GA'>F\\
r$\"3_$oKa/0\"*)**F\\r7$$\"3+pmT5!**QH#F\\r$\"33DtW0KGb()F\\r7$$\"3+-]
i!zSs&HF\\r$\"3nZ?(HWL=B(F\\r7$F`s$\"3oln97=#oO'F\\r7$Fes$\"3'fJ='p)p+
%\\F\\r7$Fjs$\"39\\mt\\$[e\\%F\\r7$F_t$\"3)Gt?>`O3.%F\\r7$Fdt$\"3![9;q
W*[%f$F\\r7$Fit$\"3ok:j&3>i5$F\\r7$F^u$\"3UZJ)e6]sl#F\\r7$Fcu$\"3OG*y[
\\&zCAF\\r7$Fhu$\"3!p5(\\U8Ep=F\\r7$F]v$\"3M]7cfM+M:F\\r7$Fbv$\"3T_K0T
*fzB\"F\\r7$Fgv$\"3-::hm`g?5F\\r7$F\\w$\"3.8Lhu,XP#)F\\s7$Faw$\"3W(3k5
sabc'F\\s7$Ffw$\"3Vf_^;T;M_F\\s7$F[x$\"3s*o)*Q4=s=%F\\s7$F`x$\"3gw.D;l
DbKF\\s7$Fex$\"3i'>-\"eS&ze#F\\s7$Fjx$\"3%y@1=w6(>?F\\s7$F_y$\"3R..Kjb
Z4;F\\s7$Fdy$\"376#*)ou?FD\"F\\s7$Fiy$\"3If]dexYv)*F]z7$F_z$\"3_\\_\\R
(*e'o(F]z7$Fdz$\"3O;APNyu0gF]z7$Fiz$\"387I#p<K/j%F]z7$F^[l$\"3yZUHQ'**
))f$F]z7$Fc[l$\"3=d`Bfx?xFF]z7$Fh[l$\"3kgz)))oL[9#F]z7$F]\\l$\"3')*GyS
kk'*o\"F]z7$Fb\\l$\"3+tdveq$RG\"F]z7$Fg\\l$\"3:Ru!4C-L+\"F]z7$F\\]l$\"
3VJ&z;.W`q(F`]l7$Fb]l$\"3S8;6avdzfF`]l7$Fg]l$\"3[\")4?iH2\\XF`]l-F\\^l
6&F^^lFa^lF_^lFa^l-%+AXESLABELSG6$Q\"t6\"Q\"yFb`m-%%VIEWG6$;F(Fg]l;$!#
5F*$\"\"%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 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 190 "We see that when a0 is 6/5e^(-1) the solution go
es towards infinity and negative infinity as t approaches zero.  When \+
a0 = e(-1), the solution goes towards zero as y goes towards infinity.
  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 0 0" 3 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }