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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "The printed version of the
 test left off a " }{XPPEDIT 18 0 "-6" ",$\"\"'!\"\"" }{TEXT -1 35 " i
n the second equation.  Fix that." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "solve(\{4*x+y+x*y=0, x-y-6\}, \{x,y\});" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "de:=\{diff(x(t),t)=4*x(t)+y(t)+x(t)
*y(t), diff(y(t),t)=x(t)-y(t)-6\};" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "subs(x(t)=u(t)-2,y(t)=v(t)-8,de); simplify(\");" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "with(linalg): A:=matrix([[-4
,-1], [1, -1]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eigenva
ls(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "So (-2,-8) is an asymptotically st
able improper node." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "subs
(x(t)=u(t)+3,y(t)=v(t)-3,de); simplify(\");" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 28 "A:=matrix([[1,4], [1, -1]]);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 13 "eigenvals(A);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 79 "So (3,-3) is a saddle point, unstable.  Here is a plot wi
th a few trajectories." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "w
ith(DEtools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 251 "DEplot([d
e[1],de[2]],[x(t),y(t)],t=-2..6,x=-4..6, y=-10..0, [[x(0)=0,y(0)=-2], \+
[x(0)=0, y(0)=-4], [x(0)=0, y(0)=-9], [x(0)=-3,y(0)=-3], [x(0)=-4,y(0)
=-10], [x(0)=4, y(0)=-4.2], [x(0)=2, y(0)=-2], [x(0)=6, y(0)=-4.6], [x
(0)=6, y(0)=-7]], stepsize=0.1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "14 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 }