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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "p. 750, #7" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "d71:=d
iff(x(t),t)=-4*x(t)+2*y(t)+8;\nd72:=diff(y(t),t)=x(t)-2*y(t)+1;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(\{x*2-4,.5*(x+1)\},x=0..4);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve(\{-4*a+2*b+8=0,a-2*b
+1=0\},\{a,b\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "subs(\{
x(t)=u(t)+3,y(t)=v(t)+2\},\{d71,d72\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "lsys:=simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 28 "A:=matrix([[-4,2], [1,-2]]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "eigenvectors(A);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
30 "Both eigenvalues are negative." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 178 "### WARNING: `dsolve` has been extensively rewritten
, many new result forms can occur and options are slightly different, \+
see help page for details\ndsolve(\{d71,d72\},\{x(t),y(t)\});" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 84 "inits:=\{[x(0)=3.5,y(0)=0], [x(0)=2.5,y(0)=0], [x(
0)=1.5,y(0)=2], [x(0)=2.5,y(0)=3]\};" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 100 "with(DEtools):\nDEplot([d71,d72],[x(t),y(t)],t=-2..6
,x=0..4,y=0..4,inits, stepsize=0.1, arrows=thin);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 5 " # 11" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 
"d111:=diff(x(t),t)=-x(t)+y(t)+8;\nd112:=diff(y(t),t)=-x(t)-4*y(t)-17;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "solve(\{-a+b+8=0,-a-4*b
-17=0\},\{a,b\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "subs(
\{x(t)=u(t)+3,y(t)=v(t)-5\},\{d111,d112\});" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 18 "lsys:=simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 29 "A:=matrix([[-1,1], [-1,-4]]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "eigenvectors(A);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "inits:=\{[x(0)=3.5,y(0)=-5], [x(0)=2.5,y(0)=-5], [x(0
)=1.5,y(0)=-4], [x(0)=2.5,y(0)=-4]\};" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 104 "with(DEtools):\nDEplot([d111,d112],[x(t),y(t)],t=-2.
.6,x=0..4,y=-7..-3,inits, stepsize=0.1, arrows=thin);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 4 "# 15" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 65 "d151:=diff(x(t),t)=x(t)+2*y(t);\nd152:=diff(y(t),t)=5
*x(t)-2*y(t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Obviously the eq
uation is already linear and homogeneous with (0,0) the only critical \+
point." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A:=matrix([[1,2],
 [5,-2]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(
A);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "One eigenvalue,  3,  is p
ositive, and the other,  -4,  is negative, so (0,0) is unstable.  (It \+
is a saddle point.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "ini
ts:=\{[x(0)=3,y(0)=0], [x(0)=2,y(0)=0], [x(0)=1,y(0)=0], [x(0)=-1,y(0)
=0], [x(0)=0,y(0)=2], [x(0)=0,y(0)=-1]\};" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 89 "DEplot([d151,d152],[x(t),y(t)],t=-2..6,x=-2..4,y=-2
..4,inits, stepsize=0.1, arrows=thin);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 4 "# 17" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "d171:=d
iff(x(t),t)=-8*x(t)+y(t);\nd172:=diff(y(t),t)=2*x(t)+2*y(t);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Obviously the equation is already \+
linear and homogeneous with (0,0) the only critical point." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A:=matrix([[-8,1], [2,2]]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(A);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 135 "One eigenvalue,  -3+3*3^(1/2),  is posit
ive, and the other,  -3-3*3^(1/2),  is negative, so (0,0) is unstable.
  (It is a saddle point.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
112 "inits:=\{[x(0)=3,y(0)=0], [x(0)=2,y(0)=0], [x(0)=1,y(0)=0], [x(0)
=-1,y(0)=0], [x(0)=0,y(0)=2], [x(0)=0,y(0)=-1]\};" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 89 "DEplot([d171,d172],[x(t),y(t)],t=-2..6,x=-2.
.4,y=-2..4,inits, stepsize=0.1, arrows=thin);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 9 "p. 762, 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 
"d11:=diff(x(t),t)=3*x(t)+2*y(t)-y(t)^2;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "d12:=diff(y(t),t)=-2*x(t)-2*y(t)+x(t)*y(t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "solve(\{3*a+2*b-b^2=0,-2*a-2
*b+a*b=0\},\{a,b\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eval
f(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "Near the origin, y^2 and
 x*y are both very small, so the linearization about (0,0) is:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 33 "d11l:=diff(x(t),t)=3*x(t)+2*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "d12l:=diff(y(t),t)=-2*x(t)-2*y(t);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "A:=matrix([[3,2], [-2,-2]]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(linalg):eigenvectors(A);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "Another saddle point!  Rats.  Lets
 do a DEplot that includes the other critical point." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 138 "inits:=\{[x(0)=.4,y(0)=-.3], [x(0)=-1,y(
0)=0], [x(0)=1,y(0)=1], [x(0)=-1,y(0)=-1], [x(0)=0,y(0)=1], [x(0)=0,y(
0)=-1], [x(0)=.3,y(0)=-0.4]\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 141 "with(DEtools):DEplot([d11,d12],[x(t),y(t)],t=-6..6,x=0..1,y=-
1..0, \{[x(0)=.3,y(0)=-.4], [x(0)=.3,y(0)=-.5],[x(0)=.3,y(0)=-.6]\}, s
tepsize=.1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;wit
h(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "v:=vector([3*
x+2*y-y^2, -2*x-2*y+x*y]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
72 "A:=matrix([[diff(v[1],x), diff(v[1],y)], [diff(v[2],x), diff(v[2],
y)]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "x:=.3670068383;y:
= -.4494897428;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(A);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(A);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "I have no idea why Maple does not \+
make the substitution in " }{XPPEDIT 18 0 "A" "6#%\"AG" }{TEXT -1 1 ".
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "762, #11" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 55 "restart:x:='x';y:='y';solve(\{a+b=0,5*b-a*b+6
=0\},\{a,b\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "d111:=dif
f(x(t),t)=x(t)+y(t);\nd112:=diff(y(t),t)=5*y(t)-x(t)*y(t)+6;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sys:=\{d111,d112\};" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "dsolve(sys,\{x(t),y(t)\});" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "simplify(subs(\{x(t)=u(t)
+3,y(t)=v(t)-3\},sys));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "
with(linalg): A:=matrix([[1,1], [3,2]]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "eigenvectors(A);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "So  \+
(3,-3)  is unstable (a saddle point)." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "simplify(subs(\{x(t)=u(t)+2,y(t)=v(t)-2\},sys));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "with(linalg): A:=matrix([[1,
1], [2,3]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvector
s(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "So (2,-2)  is  a unstable point, n
ot a saddle point." }}{PARA 0 "" 0 "" {TEXT -1 3 "#15" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "solve(\{6*a-2*a^2-a*b=0, 6*b-2*b^2-
a*b=0\},\{a,b\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "A:=mat
rix([[6,0], [0,6]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eig
envectors(A);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "(0,0 is unstable
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 224 "with(DEtools):\ninits:=\{[x(0)=2.2,y(0)=-2.2], [x(0)
=3.1,\ny(0)=-3.3], [x(0)=3, y(0)=-2.5]\};\nDEplot([diff(x(t),t)=x(t)+y
(t), diff(y(t),t)=5*y(t)-x(t)*y(t)+6],[x(t),y(t)],t=-6..6,x=0..4,y=-4.
.0,inits, stepsize=0.1, arrows=thin);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 110 "s15:=\{diff(x(t),t)=6*x(t)-2*x(t)^2-x(t)*y(t), diff(
y(t),t)=6*y(t)-2*y(t)^2-x(t)*y(t)\}; subs(x(t)=u(t)+3, s15);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A:=matrix([[-6,-3], [0,3]]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(A);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 54 "The critical point (3,0) is unstable (a s
addle point)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "subs(y(t)=
v(t)+3, s15);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A:=matrix([[3,0], [-3
,-6]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(A);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Another saddle point at (0,3)
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "subs(\{y(t)=v(t)+2,x(t
)=u(t)+2\}, s15);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simpli
fy(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "A:=matrix([[-4,-2
], [-2,-4]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvecto
rs(A);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "So  (2,2) is a stable p
oint.  Here is a plot:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 262 "with(DEtools):\ninits:=\{[x(0)=.1,
y(0)=.3], [x(0)=3.1,\ny(0)=.3], [x(0)=.3,y(0)=3.1], [x(0)=2, y(0)=2.2]
\};\nDEplot([diff(x(t),t)=6*x(t)-2*x(t)^2-x(t)*y(t), diff(y(t),t)=6*y(
t)-2*y(t)^2-x(t)*y(t)],[x(t),y(t)],t=-2..6,x=-1..4,y=-1..4,inits, step
size=0.1, arrows=thin);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "# 17  \+
This is an equation of a triode (vacuum tube) oscillator." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "restart:vdp:=diff(x(t),t,t)+epsilon
*(x(t)^2-1)*diff(x(t),t)+x(t)=0;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 165 "### WARNING: `dsolve` has been extensively rewritten
, many new result forms can occur and options are slightly different, \+
see help page for details\ndsolve(vdp,x(t));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "epsilon:=10;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 198 "### WARNING: `dsolve` has been extensively rewritten
, many new result forms can occur and options are slightly different, \+
see help page for details\nnsol:=dsolve(\{vdp,x(0)=1,D(x)(0)=0\},x(t),
numeric);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nsol(1);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nsol(100);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 84 "inits:=\{[x(0)=.1,y(0)=.3], [x(0)=.6,\ny(
0)=.6], [x(0)=.8,y(0)=.8], [x(0)=1, y(0)=1]\};" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 243 "with(DEtools): DEplot([diff(x(t),t)=y(t), dif
f(y(t),t)=-x(t)-epsilon*x(t)^2*y(t)+epsilon*x(t)], [x(t),y(t)], t=0..1
0, x=-2..4, y=-2..2, inits, stepsize=.0151); # Experiement with differ
ent values of epsilon.  The stepsize has to be very small." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "inits:=\{[x(0)=.1,y(0)=.01], [x(0)=
.2,\ny(0)=.02], [x(0)=.3,y(0)=.03], [x(0)=0.2, y(0)=.05]\};" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "A:=1/4; B:=1/2; a_1:=1; a_2
:=1; d_1:=4; d_2:=3; solve(\{a_1*x*(1-x/A-d_1*y/A),a_2*y*(1-y/B-d_2*x/
B)\},\{x,y\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "DEplot([
diff(x(t),t)=a_1*x(t)*(1-x(t)/A-d_1*y(t)/A), diff(y(t),t)=a_2*y(t)*(1-
y(t)/B-d_2*x(t)/B)], [x(t),y(t)], t=0..6, x=0..14/44, y=0..2/44, inits
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "So the point (7, 1)/44 look
s like a saddle point." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 26 "Project C, p. 802, part a." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(\{(7-x)/2, 5-x\},x=0..10);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve(\{y=(7-x)/2, 5-x=y\},
\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 85 "inits:=\{[x(0)=1,y(0)=3.7], [x(0)=1,\ny(0)=1
.5], [x(0)=4,y(0)=3], [x(0)=5.5, y(0)=.5]\};" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "DEplot
([diff(x(t),t)=x(t)*(7-x(t)-2*y(t)),diff(y(t),t)=y(t)*(5-x(t)-y(t))], \+
[x(t),y(t)], t=-1..3, x=0..7, y=0..5, inits, stepsize=.1);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 7 "Part b." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 81 "inits:=\{[x(0)=.5,y(0)=0], [x(0)=1,y(0)=0], [x(0)=1.5
,y(0)=0], [x(0)=-1,y(0)=.5]\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 101 "DEplot([diff(x(t),t)=y(t), diff(y(t),t)=-x(t)+x(t)^3], [x(t),
y(t)], t=0..6, x=-2..2, y=-2..2, inits);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "dsolve(\{diff(x(t),t)=y(t), diff(y(t),t)=-x(t)+x(t)^3
\},\{x(t),y(t)\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 190 "### \+
WARNING: `dsolve` has been extensively rewritten, many new result form
s can occur and options are slightly different, see help page for deta
ils\ndsolve(diff(x(t),t,t)+x(t)-x(t)^3=0,x(t));" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 7 "Part c." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "DEplot([diff(x(t),t)=y
(t), diff(y(t),t)=-x(t)-5*(x(t)^2-1)*y(t)], [x(t),y(t)], t=0..6, x=-2.
.2, y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "A:=matrix([[1,1], [-1,1]]);w
ith(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvector
s(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 259 "DEplot([diff(x(t)
,t)=-y(t)+x(t)*(1-x(t)^2-y(t)^2)*(4-x(t)^2-y(t)^2), diff(y(t),t)=x(t)+
y(t)*(1-x(t)^2-y(t)^2)*(4-x(t)^2-y(t)^2)],[x(t),y(t)], t=0..5, x=-2..2
, y=-2..2, \{[x(0)=2, y(0)=0],[x(0)=2.1, y(0)=0],[x(0)=1.9, y(0)=0],[x
(0)=.25, y(0)=0]\}, stepsize=.01);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "130" 0 }{VIEWOPTS 1 1 0 3 2 1804 }