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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "The maple process of solving" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "    y\" \+
= y' + 2y + cos(x),    x in  [0, Pi/2]" }}{PARA 0 "" 0 "" {TEXT -1 35 
"        y(0) = -0.3,   y(Pi/2)=-0.1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
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1 0 7 "a:=0.0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "b:=evalf(Pi/2);         # Ca
pital P" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"+Fjzq:!\"*" }}}
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "h:=(b-a)/n;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"hG$\"+aEfTJ!#5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "x:=array(0..n,[ seq(a+i*h,i=0..n) ]);" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%\"xG-%&ARRAYG6$7#;\"\"!\"\"&7(/6#F*F*/6#\"\"\"$
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"solve( \{ y[0]=-0.3,\nseq(    (2-h)*y[i+1]-4*(1+h^2)*y[i]+(2+h)*y[i-1
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!+++++I!#5/&F&6#\"\"&$!+++++5F+/&F&6#\"\"\"$!+!4/Q;$F+/&F&6#\"\"%$!+^u
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 " 0 "" {MPLTEXT 1 0 44 "assign(%);   # assigning above values to y's
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{TEXT -1 25 "We want to see the graph:" }}{PARA 0 "" 0 "" {TEXT -1 0 "
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{PARA 0 "" 0 "" {TEXT -1 49 "We happen to know the exact solution in a
 formula" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
31 "    y(x) = -(sin(x)+3cos(x))/10" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 27 "Let's compare the solution." }}{PARA 0 "
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