{VERSION 1 0 "NEXTSTEP" "1.0"}{GLOBALS 1 0}{FONT 0 "Times-Roman" 
"Times" "Times-Roman" 4 12 64 "Times-Roman" 12}{FONT 1 "Ohlfs" "O
hlfs" "Courier" 4 12 192 "Ohlfs" 12}{FONT 2 "Courier-Bold" "Couri
er" "Courier-Bold" 8 12 192 "Courier-Bold" 12}{SCP_R 1 0 20{COM_R
 2 0{TEXT 0 24 "15 Minute Maple\012Lesson 3"}{NXRTF 0 234 "\{\\rt
f0\\ansi\{\\fonttbl\\f0\\fnil Times-Roman;\}\012\\margl40\012\\ma
rgr40\012\{\\colortbl;\\red255\\green255\\blue255;\}\012\\cb1\\pa
rd\\tx480\\tx960\\tx1440\\tx1920\\tx2400\\tx2880\\tx3360\\tx3840\
\tx4320\\tx4800\\f0\\b0\\i0\\ulnone\\fs24\\fc0\\cf0 15 Minute Map
le\\\012Lesson 3\012\}\012"}}{COM_R 3 0{TEXT 0 161 "Steven R. Dun
bar\012Departmetn of Mathematics and Statistics\012University of 
Nebraska-Lincoln\012Lincoln, NE 68588\012\012sdunbar@math.unl.edu
\012http://www.math.un.edu/~sdunbar\012"}{NXRTF 0 377 "\{\\rtf0\\
ansi\{\\fonttbl\\f0\\fnil Times-Roman;\}\012\\margl40\012\\margr4
0\012\{\\colortbl;\\red255\\green255\\blue255;\}\012\\cb1\\pard\\
tx480\\tx960\\tx1440\\tx1920\\tx2400\\tx2880\\tx3360\\tx3840\\tx4
320\\tx4800\\f0\\b0\\i0\\ulnone\\fs24\\fc0\\cf0 Steven R. Dunbar\
\\012Departmetn of Mathematics and Statistics\\\012University of 
Nebraska-Lincoln\\\012Lincoln, NE 68588\\\012\\\012sdunbar@math.u
nl.edu\\\012http://www.math.un.edu/~sdunbar\\\012\012\}\012"}}
{COM_R 4 0{TEXT 0 153 "Topics:  differntial equations, substituti
ons, \012\012Title:  Lesson 3\012\012Keywords: dsolve, rhs\012\01
2Audience:  Students in Computer Lab Setting\012\012Tine:  15 min
utes\012"}{NXRTF 0 371 "\{\\rtf0\\ansi\{\\fonttbl\\f0\\fnil Times
-Roman;\}\012\\margl40\012\\margr40\012\{\\colortbl;\\red255\\gre
en255\\blue255;\}\012\\cb1\\pard\\tx480\\tx960\\tx1440\\tx1920\\t
x2400\\tx2880\\tx3360\\tx3840\\tx4320\\tx4800\\f0\\b0\\i0\\ulnone
\\fs24\\fc0\\cf0 Topics:  differntial equations, substitutions, \
\\012\\\012Title:  Lesson 3\\\012\\\012Keywords: dsolve, rhs\\\01
2\\\012Audience:  Students in Computer Lab Setting\\\012\\\012Tin
e:  15 minutes\\\012\012\}\012"}}{COM_R 5 0{TEXT 0 117 "Maple Tip
:  It is usualy helpful to assign (with := ) a name or label to e
verything in Maple, so you can refer to it."}{NXRTF 0 326 "\{\\rt
f0\\ansi\{\\fonttbl\\f0\\fnil Times-Roman;\}\012\\margl40\012\\ma
rgr40\012\{\\colortbl;\\red255\\green255\\blue255;\}\012\\cb1\\pa
rd\\tx480\\tx960\\tx1440\\tx1920\\tx2400\\tx2880\\tx3360\\tx3840\
\tx4320\\tx4800\\f0\\b0\\i0\\ulnone\\fs24\\fc0\\cf0 Maple Tip:  I
t is usualy helpful to assign (with := ) a name or label to every
thing in Maple, so you can refer to it.\012\}\012"}}{COM_R 6 0
{TEXT 0 390 "A (first-order) differential equation is an equation
 about a function and it's derivatives.\012\012In Maple, we write
 a function the way we would in mathematics: say f(t)\012\012Usua
lly in Maple, it is convenient to assign a name to any equation w
e want to solve, including a differential equation:\012Note the d
ifference betweent the assignment of the name with := and the equ
ality symbol of the equation"}{NXRTF 0 604 "\{\\rtf0\\ansi\{\\fon
ttbl\\f0\\fnil Times-Roman;\}\012\\margl40\012\\margr40\012\{\\co
lortbl;\\red255\\green255\\blue255;\}\012\\cb1\\pard\\tx480\\tx96
0\\tx1440\\tx1920\\tx2400\\tx2880\\tx3360\\tx3840\\tx4320\\tx4800
\\f0\\b0\\i0\\ulnone\\fs24\\fc0\\cf0 A (first-order) differential
 equation is an equation about a function and it's derivatives.\\
\012\\\012In Maple, we write a function the way we would in mathe
matics: say f(t)\\\012\\\012Usually in Maple, it is convenient to
 assign a name to any equation we want to solve, including a diff
erential equation:\\\012Note the difference betweent the assignme
nt of the name with := and the equality symbol of the equation\01
2\}\012"}}{INP_R 7 0 "> "{TEXT 1 30 "de := diff(f(t), t) = -2*f(t
);"}}{OUT_R 8 0 7{DAG :3n3\`de`=3(3n4\`diff`,3(3n3\`f`,2n3\`t`pD+
3p9i2x0002}}{COM_R 9 0{TEXT 0 106 "We solve a differential equati
on with the dsolve command, requiring the equation and the unknow
n function."}{NXRTF 0 315 "\{\\rtf0\\ansi\{\\fonttbl\\f0\\fnil Ti
mes-Roman;\}\012\\margl40\012\\margr40\012\{\\colortbl;\\red255\\
green255\\blue255;\}\012\\cb1\\pard\\tx480\\tx960\\tx1440\\tx1920
\\tx2400\\tx2880\\tx3360\\tx3840\\tx4320\\tx4800\\f0\\b0\\i0\\uln
one\\fs24\\fc0\\cf0 We solve a differential equation with the dso
lve command, requiring the equation and the unknown function.\012
\}\012"}}{INP_R 10 0 "> "{TEXT 1 26 "soln := dsolve( de, f(t));"}
}{OUT_R 11 0 10{DAG =3(3n3\`f`,2n3\`t`*5(3n3\`exp`,2+3p5i2x0002j2
x0001n3\`_C1`p10}}{COM_R 12 0{TEXT 0 260 "Notice the arbitrary co
nstant that comes up natually from the integration.\012\012We can
 eliminate the unknown constant if we know one additional piece o
f information about the solution, like it's intial condition.\012
Note how we assign a name to the initial condition."}{NXRTF 0 472
 "\{\\rtf0\\ansi\{\\fonttbl\\f0\\fnil Times-Roman;\}\012\\margl40
\012\\margr40\012\{\\colortbl;\\red255\\green255\\blue255;\}\012\
\cb1\\pard\\tx480\\tx960\\tx1440\\tx1920\\tx2400\\tx2880\\tx3360\
\tx3840\\tx4320\\tx4800\\f0\\b0\\i0\\ulnone\\fs24\\fc0\\cf0 Notic
e the arbitrary constant that comes up natually from the integrat
ion.\\\012\\\012We can eliminate the unknown constant if we know 
one additional piece of information about the solution, like it's
 intial condition.\\\012Note how we assign a name to the initial 
condition.\012\}\012"}}{INP_R 13 0 "> "{TEXT 1 15 "ic := f(0) = 3
;"}}{OUT_R 14 0 13{DAG :3n3\`ic`=3(3n3\`f`,2j2x0000j2x0003}}
{COM_R 15 0{TEXT 0 127 "We can solve the differential equation an
d the initial condition all in one command:\012\012Note how I ass
ign a name to the solution."}{NXRTF 0 338 "\{\\rtf0\\ansi\{\\font
tbl\\f0\\fnil Times-Roman;\}\012\\margl40\012\\margr40\012\{\\col
ortbl;\\red255\\green255\\blue255;\}\012\\cb1\\pard\\tx480\\tx960
\\tx1440\\tx1920\\tx2400\\tx2880\\tx3360\\tx3840\\tx4320\\tx4800\
\f0\\b0\\i0\\ulnone\\fs24\\fc0\\cf0 We can solve the differential
 equation and the initial condition all in one command:\\\012\\\0
12Note how I assign a name to the solution.\012\}\012"}}{INP_R 16
 0 "> "{TEXT 1 32 "soln := dsolve( \{de, ic\}, f(t));"}}{OUT_R 17
 0 16{DAG :3n4\`soln`=3(3n3\`f`,2n3\`t`+3(3n3\`exp`,2+3p9i2x0002j
2x0003}}{COM_R 18 0{TEXT 0 267 "The solution of a differential eq
uation is another equation, often equating the function to an exp
licit solution expression.\012\012What we usually want is the exp
licit solution expression on the right side.  Use the rhs( ) oper
ator to pick off the stuff on the right side."}{NXRTF 0 478 "\{\\
rtf0\\ansi\{\\fonttbl\\f0\\fnil Times-Roman;\}\012\\margl40\012\\
margr40\012\{\\colortbl;\\red255\\green255\\blue255;\}\012\\cb1\\
pard\\tx480\\tx960\\tx1440\\tx1920\\tx2400\\tx2880\\tx3360\\tx384
0\\tx4320\\tx4800\\f0\\b0\\i0\\ulnone\\fs24\\fc0\\cf0 The solutio
n of a differential equation is another equation, often equating 
the function to an explicit solution expression.\\\012\\\012What 
we usually want is the explicit solution expression on the right 
side.  Use the rhs( ) operator to pick off the stuff on the right
 side.\012\}\012"}}{INP_R 19 0 "> "{TEXT 1 20 "explic := rhs(soln
);"}}{OUT_R 20 0 19{DAG :3n4\`explic`+3(3n3\`exp`,2+3n3\`t`i2x000
2j2x0003}}{INP_R 21 0 "> "{TEXT 1 0 ""}}}{END}