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{SECT 0 {EXCHG {PARA 261 "" 0 "" {TEXT -1 9 "John Cole" }}{PARA 262 "
" 0 "" {TEXT -1 22 "Differential Equations" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 256 9 "Problem 5" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 96 "A tan
k contains 100 gallons of water and 50 oz of salt.  Water containg a s
alt concentration of " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "co
ncin := (1/4)*(1+(1/2)*sin(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'
concinG,&#\"\"\"\"\"%F'*&#F'\"\")F'-%$sinG6#%\"tGF'F'" }}}{EXCHG 
{PARA 257 "" 0 "" {TEXT -1 99 "flows into the tank at a rate of 2 gal/
min, and the mixture in the tank flows out at the same rate." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 51 "A. Fi
nd the amount of salt in the tank at any time." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "The initial amoun
t of salt in the tank is 50 oz.  Salt flows in" }}{PARA 0 "" 0 "" 
{TEXT -1 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 41 "saltcontent := (1/2)*(1+(1/2)*sin(t))+50;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,saltcontentG,&#\"$,\"\"\"#\"\"\"*&#
F)\"\"%F)-%$sinG6#%\"tGF)F)" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 113 
"B.  Plot the solution for a time period that is long enough that you \+
can see the ultimate behaviour of the graph." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot(saltcontent, t=0..15
, y=50..51);" }}{PARA 13 "" 1 "" {GLPLOT2D 671 299 299 {PLOTDATA 2 "6%
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45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 260 "" 0 "" {TEXT 
-1 154 "C.  The long time behaviour of the solution is an oscillation \+
about a certain constant level.  What is this level?  What is the ampl
itude of oscillations?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 180 "The osci
llations have a peak salt content of 50.75 oz. and a low salt content \+
of 50.25 oz.  The salt content oscillates around 50.50 oz. and the amp
litude of oscillation is .25 oz." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}
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