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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Maple Project #2" }}{PARA 
0 "" 0 "" {TEXT -1 16 "Problem Set B #9" }}{PARA 0 "" 0 "" {TEXT -1 
12 "Katie Causby" }}{PARA 0 "" 0 "" {TEXT -1 12 "Amanda Smith" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 251 "
For each equation below plot the directional field and show its equili
brium points.  Find the equilibria and state whether each one is stabl
e or unstable.  Use fsolve to determine the precise value of the equil
ibruim points from the directional field." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 222 "To solve each equation we differentiated and then plotte
d the directional field.  The directional field gives the points at wh
ich the slope of the tangent line equals zero.  These points could be \+
either stable or unstable." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 132 "Wh
en we used fsolve, we set the equations equal to zero because the slop
e of the tangent line equals zero at the equilibruim points." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG 
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" 0 "" {MPLTEXT 1 0 100 "dfieldplot(diff(x(t),t)=((-x(t)*(x(t)-2)*(x(t
)-4))/10),x(t),t=-5..5,x=-4..8,arrows=LINE,axes=BOXED);" }}{PARA 13 "
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o get the exact answer we did fsolve, and Maple confirmed that the equ
ilibrium points are at zero, two, and four.  The critical point at fou
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s unstable because they move away from the horizontal line at 2, and t
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{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 236 "We did the field
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e equilibria to be 2.7 and .3 by looking at the graph.  To get the exa
ct answer we did fsolve, and Maple confirmed that the equilibrium poin
ts are at " }{XPPEDIT 18 0 ".38196601132.618033989;" "6#%#%?G" }{TEXT 
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e toward that point and the critical point at 2.6180 is unstable becau
se they move away from the horizontal line." }}}{EXCHG {PARA 0 "> " 0 
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9 1 2 2 1 45 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 399 "We did the field plot of 0.1y-siny and Maple returned \+
the graph above.  We estimated the equilibria to be zero and +/- Pi by
 looking at the graph.  To get the exact answer we did fsolve and Mapl
e returned only zero.  The critical point at zero is stable because th
ey converge toward that point. However, Maple didn't return any Pi sol
ution which would conclude that  they are not equilibria points. " }}}
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1803 }