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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 279 16 "Direction Fields" }}
{PARA 258 "" 0 "" {TEXT 280 9 "Exercises" }}{PARA 258 "" 0 "" {TEXT 
256 4 "HW 1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 257 "" 0 
"" {TEXT -1 260 "Click on a [+]  sign to expand a section. Click on a \+
[-] sign to collapse a section. To do these exercises you will have to
 insert execution groups. That can be done by clicking on the toolbar \+
icon that looks like \"[>\". It can also be done via the Insert menu.
" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Introduction" }}{PARA 0 "" 
0 "" {TEXT -1 9 "In this  " }{TEXT 257 5 "MAPLE" }{TEXT -1 3 "   " }
{HYPERLNK 17 "worksheet" 2 "worksheet" "" }{TEXT -1 28 ",  you will be
 asked to use " }{TEXT 311 5 "MAPLE" }{TEXT -1 75 "  to plot direction
 fields of first order differential equations.  The main" }{TEXT 312 
7 "  MAPLE" }{TEXT -1 32 "   function that will be used is" }{TEXT 
258 2 "  " }{TEXT 313 10 "dfieldplot" }{TEXT -1 48 ".  Information on,
 and examples of, the use of  " }{TEXT 259 10 "dfieldplot" }{TEXT -1 
45 "  may be found in the (read-only) worksheet  " }{HYPERLNK 17 "1.3e
pR4.mws" 1 "1.3epR4.mws" "" }{TEXT -1 2 ". " }}}{SECT 0 {PARA 3 "" 0 "
" {TEXT -1 62 "Exercise 1  Checking that a Differential Equation is Sa
tisfied" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 324 
18 "Backgroud Reading:" }{TEXT -1 21 " The section titled \"" }{TEXT 
325 30 "A Simple Differential Equation" }{TEXT -1 17 "\" of worksheet \+
  " }{HYPERLNK 17 "1.1epR4.mws" 1 "1.1epR4.mws" "" }{TEXT -1 3 ".  " }
}{PARA 0 "" 0 "" {TEXT -1 59 "                                       T
he help pages for  " }{HYPERLNK 17 "subs" 2 "subs" "" }{TEXT -1 8 "  a
nd   " }{HYPERLNK 17 "testeq" 2 "testeq" "" }{TEXT -1 1 "." }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "Use   " }{TEXT 
295 5 "MAPLE" }{TEXT -1 8 "   to   " }{HYPERLNK 17 "verify" 2 "testeq
" "" }{TEXT -1 9 "   that  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT 293 26 "                          " }{TEXT 296 15 "y(x
) = exp(1/x)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 42 "is a solution of the differential equation" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 5 "     " }{TEXT 297 8 "        " }{XPPEDIT 298 1 "x^4 * diff( y(x)
, x,x) + 2x^3 *diff(y(x),x) - y(x) = 0" "/,(*&%\"xG\"\"%-%%diffG6%-%\"
yG6#F%F%F%\"\"\"F-*(\"\"#F-*$F%\"\"$F--F(6$-F+6#F%F%F-F--F+6#F%!\"\"\"
\"!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 294 1 " \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "subs(y(x) = exp(1/x),  x^4*d
iff(y(x),x$2)+2*x^3*diff(y(x),x)-y(x)=0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,(*&%\"xG\"\"%-%%diffG6$-F)6$-%$expG6#*$F&!\"\"F&F&\"
\"\"F2*&F&\"\"$F+F2\"\"#F-F1\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "testeq(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%true
G" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 361 81 "Be
tter practice is to name complicated expressions so that you can refer
 to them!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 "ode := x^4*diff(y(x), x$2)+2*x^3*diff(y(x), x) - y(x)
 = 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/,(*&%\"xG\"\"%-%%diff
G6$-F+6$-%\"yG6#F(F(F(\"\"\"F2*&F(\"\"$F-F2\"\"#F/!\"\"\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "soln := y(x) = exp(1/x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG/-%\"yG6#%\"xG-%$expG6#*$F)!\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "subs(soln, ode); # Su
bstitutes exp(1/x) for every occurrence of y(x) in ode" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/,(*&%\"xG\"\"%-%%diffG6$-F)6$-%$expG6#*$F&!\"\"F&
F&\"\"\"F2*&F&\"\"$F+F2\"\"#F-F1\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "testeq(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%true
G" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{SECT 0 {PARA 259 "" 0 "" {TEXT -1 36 "Exercise 2   Free Fall Under G
ravity" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 326 
18 "Backgroud Reading:" }{TEXT -1 14 "  Worksheet   " }{HYPERLNK 17 "1
.3epR4.mws" 1 "1.3epR4.mws" "" }{TEXT -1 3 ".  " }}{PARA 0 "" 0 "" 
{TEXT -1 59 "                                       The help pages for
  " }{HYPERLNK 17 "dfieldplot" 2 "DEtools[dfieldplot]" "" }{TEXT -1 8 
"  and   " }{HYPERLNK 17 "display" 2 "plots[display]" "" }{TEXT -1 1 "
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 270 "" 0 "" {TEXT -1 124 "If an object is subject only to the fo
rce of the Earth's gravity, then the differential equation that relate
s its velocity  " }{TEXT 300 1 "v" }{TEXT 303 1 " " }{TEXT -1 14 " (me
asured in " }{TEXT 299 3 "m/s" }{TEXT -1 21 ") and  its distance  " }
{TEXT 301 1 "r" }{TEXT -1 43 "  from the earth's center  in (measured \+
in " }{TEXT 302 2 "m)" }{TEXT -1 4 ", is" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "  \+
                                " }{TEXT 327 3 "   " }{TEXT 330 3 "   \+
" }{TEXT 329 8 "        " }{XPPEDIT 328 1 "diff(v(r),r) = - g*R^2/v(r)
/r^2" "/-%%diffG6$-%\"vG6#%\"rGF),$**%\"gG\"\"\"*$%\"RG\"\"#F--F'6#F)!
\"\"*$F)F0F3F3" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Here    " }{TEXT 305 1 "g
" }{TEXT 309 1 " " }{TEXT 306 6 "= 9.81" }{TEXT 304 6 " m/s/s" }{TEXT 
-1 10 "     and  " }{TEXT 307 13 "  R = 6378000" }{TEXT -1 1 " " }
{TEXT 308 1 "m" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 18 "a
) Direction Field" }}{PARA 0 "" 0 "" {TEXT -1 71 "Plot the direction f
ield of this differential equation in the window   " }{TEXT 292 39 "[ \+
6378000 , 20000000 ] x [ 50 , 12000 ]" }{TEXT -1 1 "." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "restart: \+
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1 0 40 "ode := diff(v(r), r) = - g*R^2/v(r)/r^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$odeG/-%%diffG6$-%\"vG6#%\"rGF,,$**%\"gG\"\"\"%\"RG\"
\"#F)!\"\"F,!\"#F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "g := \+
9.81:   R := 6378000:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "df
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{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 0 {PARA 260 "
" 0 "" {TEXT -1 58 "Exercise 3 Direction Field Project From Edwards an
d Penney" }}{PARA 0 "" 0 "" {TEXT -1 21 "First,  restart the  " }
{TEXT 347 5 "MAPLE" }{TEXT -1 22 "  kernel and load the " }{TEXT 348 
7 "DEtools" }{TEXT -1 68 " package. (Place the cursor anywhere in the \+
next line and press the " }{TEXT 349 5 "Enter" }{TEXT -1 6 " key.)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "restart:   with(DEtools):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 34 "Consider the differential equation" }}
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "ode := diff(y(x), x) = sin(x
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"" }}{PARA 0 "" 0 "" {TEXT -1 110 "Don't forget to execute the precedi
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 the " }{TEXT 350 5 "Enter" }{TEXT -1 6 " key.)" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "
" {TEXT -1 51 "a) Using the Direction Field Plot to Spot Solutions" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 5 "Use  " }{TEXT 352 10 "dfieldplot" }{TEXT -1 76 "
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dow   " }{TEXT 353 21 "[-10, 10] x [-10, 10]" }{TEXT -1 4 " .  " }}
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