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{SECT 0 {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 54 "     MAPLE COMMANDS F
OR SOLVING DIFFERENTIAL EQUATIONS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT -1 54 "The first two commands are to lo
ad the MAPLE routines." }{TEXT 256 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "with(DEtools):with(plots):" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 257 68 "There are three basic commands for processing DEs
 that you will use." }}{PARA 0 "" 0 "" {TEXT -1 51 "I. Plotting direct
ion fields (and sample solutions)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
67 "DEplot(\{diff(y(x),x)-x^5*y(x)*cos(x)=0\},[y(x)],x=-1..1,[[y(0)=1]
]);" }}{PARA 0 "" 0 "" {TEXT -1 28 "There are five major fields:" }}
{PARA 0 "" 0 "" {TEXT -1 55 "     (a) a DE of any order or system of f
irst order DEs" }}{PARA 0 "" 0 "" {TEXT -1 25 "     (b) UNKNOWN functi
on" }}{PARA 0 "" 0 "" {TEXT -1 16 "     (c) x-range" }}{PARA 0 "" 0 "
" {TEXT -1 87 "     (d) A LIST of sets of initial conditions: each set
 of initial conditions is a LIST" }}{PARA 0 "" 0 "" {TEXT -1 70 "     \+
(e) Options:  eg.  colour=black, linecolour=[blue], arrows='NONE'" }}
{PARA 0 "" 0 "" {TEXT -1 107 "If the DE is first order, or a system of
 two first order autonomous DEs, a Direction field is plotted.  For" }
}{PARA 0 "" 0 "" {TEXT -1 74 "each list of initial conditions,  a grap
h of the solution will be plotted." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 37 "II Plotting time portrait of solution" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 128 "phaseportrait([diff(y(t),t)-t^5*y(t)*cos(t)=0],
[y(t)],t=0..1,[[y(0)=1]],stepsize=.1,scene=[t,y(t)],linecolor=black,ar
rows=NONE);" }}{PARA 0 "" 0 "" {TEXT -1 52 "For this routine, the inde
pendent variable must be  " }{MPLTEXT 0 21 1 "t" }{TEXT -1 63 " ; this
 gives a graph of the solution on the selected interval." }}{PARA 0 "
" 0 "" {TEXT -1 70 "The fields are otherwise similar to those for eith
er DEplot or dsolve." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 25 " III Formula for solution" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "dsolve(\{diff(y(x),x$2)-y(x)=0,y(0)=1,D(y)(0)=2\},y(x
));" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "There are three maj
or fields:" }}{PARA 0 "" 0 "" {TEXT -1 51 "     (a) DE or system of DE
s and Initial Conditions" }}{PARA 0 "" 0 "" {TEXT -1 57 "     (b) UNKN
OWN function for which a formula is required" }}{PARA 0 "" 0 "" {TEXT 
-1 16 "     (c) Options" }}{PARA 0 "" 0 "" {TEXT -1 77 "The result is \+
a formula for the solution IF A FORMULA EXISTS.  If there is no" }}
{PARA 0 "" 0 "" {TEXT -1 31 "formula, no result is produced." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "MAKE SURE A SEM
I-COLON (;)  IS USED AT THE END OF THE COMMAND TO GET A RESULT." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 41 "(The solution may be plotted as follows.)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 34 "plot((3*exp(x)-exp(-x))/2,x=0..1);" }}}}{MARK "1 1 1" 0 }
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