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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "with(DEtools):\nwith
(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "# Ch. 6.12 Ex.
 21 part a) \nslopefield:=DEplot( diff(y(x),x)=x+y(x), \n  y(x), x=-4.
.4, y=-4..4 , arrows=line):\ndisplay(slopefield);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 72 "# Ch. 6.12 Ex. 21 part b)\nsolution:=dsolve(
 diff(y(x),x)=x+y(x), y(x) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 355 "# Ch. 6.12 Ex. 21 part c)\n# This extracts the right hand side \+
of the above equation y(x)=...\nop(2,solution);\nf1 := subs(_C1=-2, op
(2,solution) );\nf2 := subs(_C1=-1, op(2,solution) );\nf3 := subs(_C1=
 0, op(2,solution) );\nf4 := subs(_C1= 1, op(2,solution) );\nf5 := sub
s(_C1= 2, op(2,solution) );\ndisplay( slopefield, plot([f1,f2,f3,f4,f5
],x=-4..4, -4..4) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "# \+
Ch. 6.12 Ex. 21 part d) \nsolution:=dsolve( \{diff(y(x),x)=x+y(x), y(0
)=-7/10\}, y(x) );\nf:=op(2,solution);\nsolutiongraph:=plot(f, x=0..1)
:\ndisplay(solutiongraph);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
288 "# Ch. 6.12 Ex. 21 part e)  \neuler4 := dsolve( \{diff(y(x),x)=x+y
(x), y(0)=-7/10\}, y(x), \n                  numeric, method=classical
[foreuler], stepsize=1/4);\neuler4plot:= plot( 'op([2,2],euler4(x))', \+
x=0..1, adaptive=false, numpoints=5 , color=yellow):\ndisplay(solution
graph, euler4plot);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 777 "# C
h. 6.12 Ex. 21 part f) \neuler8 := dsolve( \{diff(y(x),x)=x+y(x), y(0)
=-7/10\}, y(x), \n                  numeric, method=classical[foreuler
], stepsize=1/8);\neuler8plot:= plot( 'op([2,2],euler8(x))', x=0..1, a
daptive=false, numpoints=9 , color=cyan):\n\neuler16:= dsolve( \{diff(
y(x),x)=x+y(x), y(0)=-7/10\}, y(x), \n                  numeric, metho
d=classical[foreuler], stepsize=1/16);\neuler16plot:=plot( 'op([2,2],e
uler16(x))', x=0..1, adaptive=false, numpoints=17, color=green):\n\neu
ler32:= dsolve( \{diff(y(x),x)=x+y(x), y(0)=-7/10\}, y(x), \n         \+
         numeric, method=classical[foreuler], stepsize=1/32);\neuler32
plot:=plot( 'op([2,2],euler32(x))', x=0..1, adaptive=false, numpoints=
33, color=blue):\n\ndisplay(solutiongraph, euler4plot, euler8plot, eul
er16plot, euler32plot);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 943 
"# Ch. 6.12 Ex. 21 part g) \neuler4 := dsolve( \{diff(y(x),x)=x+y(x), \+
y(0)=-7/10\}, y(x), \n                  numeric, method=classical[fore
uler], stepsize=1/4);\neuler8 := dsolve( \{diff(y(x),x)=x+y(x), y(0)=-
7/10\}, y(x), \n                  numeric, method=classical[foreuler],
 stepsize=1/8);\neuler16:= dsolve( \{diff(y(x),x)=x+y(x), y(0)=-7/10\}
, y(x), \n                  numeric, method=classical[foreuler], steps
ize=1/16);\neuler32:= dsolve( \{diff(y(x),x)=x+y(x), y(0)=-7/10\}, y(x
), \n                  numeric, method=classical[foreuler], stepsize=1
/32);\nf4 := op([2,2],euler4(1) );\nf8 := op([2,2],euler8(1) );\nf16:=
 op([2,2],euler16(1));\nf32:= op([2,2],euler32(1));\nfexact:= evalf( s
ubs(x=1, f) );\n\nerror4:= fexact-f4;\nerror8:= fexact-f8;\nerror16:= \+
fexact-f16;\nerror32:= fexact-f32;\n\npercentageerror4 := (fexact-f4 )
/fexact;\npercentageerror8 := (fexact-f8 )/fexact;\npercentageerror16:
= (fexact-f16)/fexact;\npercentageerror32:= (fexact-f32)/fexact;\n" }}
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