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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 24 "15 Minute Maple\nLesson 3

" }}}{EXCHG {PARA 19 "" 0 "" {TEXT -1 161 "Steven R. Dunbar\nDepartmet

n of Mathematics and Statistics\nUniversity of Nebraska-Lincoln\nLinco

ln, NE 68588\n\nsdunbar@math.unl.edu\nhttp://www.math.un.edu/~sdunbar

\n" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 153 "Topics:  differntial equ

ations, substitutions, \n\nTitle:  Lesson 3\n\nKeywords: dsolve, rhs\n

\nAudience:  Students in Computer Lab Setting\n\nTine:  15 minutes\n" 

}}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 117 "Maple Tip:  It is usualy hel

pful to assign (with := ) a name or label to everything in Maple, so y

ou can refer to it." }}{PARA 256 "" 0 "" {TEXT -1 93 "A (first-order) \+

differential equation is an equation about a function and it's derivat

ives.\n\n" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 30 "Solving Differentia

l Equations" }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 297 "In Maple, we wri

te a function the way we would in mathematics: say f(t)\n\nUsually in \+

Maple, it is convenient to assign a name to any equation we want to so

lve, including a differential equation:\nNote the difference betweent \+

the assignment of the name with := and the equality symbol of the equa

tion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "de := diff(f(t), t)

 = -2*f(t);" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 106 "We solve a diff

erential equation with the dsolve command, requiring the equation and \+

the unknown function." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "so

ln := dsolve( de, f(t));" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 260 "No

tice the arbitrary constant that comes up natually from the integratio

n.\n\nWe can eliminate the unknown constant if we know one additional \+

piece of information about the solution, like it's intial condition.\n

Note how we assign a name to the initial condition." }}}{EXCHG {PARA 

0 "> " 0 "" {MPLTEXT 1 0 15 "ic := f(0) = 3;" }}}{EXCHG {PARA 256 "" 

0 "" {TEXT -1 127 "We can solve the differential equation and the init

ial condition all in one command:\n\nNote how I assign a name to the s

olution." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "soln := dsolve(

 \{de, ic\}, f(t));" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 267 "The sol

ution of a differential equation is another equation, often equating t

he function to an explicit solution expression.\n\nWhat we usually wan

t is the explicit solution expression on the right side.  Use the rhs(

 ) operator to pick off the stuff on the right side." }}}{EXCHG {PARA 

0 "> " 0 "" {MPLTEXT 1 0 20 "explic := rhs(soln);" }}}{EXCHG {PARA 0 "

> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "4 0 0" 30 }{VIEWOPTS 1 1 0 1 1 

1803 }