(*^
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Assignment #4
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EMStep[{t_,y_}] := N[{t+h,y+h*f[t,y]}];
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SetOptions[ListPlot,PlotJoined->True];
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1. y'[t] == 2 y[t] - 1, y[0] == 1
;[s]
2:0,0;3,1;34,-1;
2:1,13,9,Times,1,12,0,0,0;1,13,10,Courier,1,12,0,0,0;
:[font = input; preserveAspect]
f[t_,y_] = 2*y - 1;
:[font = input; preserveAspect]
 h = 0.1;
;[s]
2:0,1;1,0;10,-1;
2:1,12,10,Courier,1,12,0,0,0;1,12,9,Times,0,12,0,0,0;
:[font = input; preserveAspect; startGroup]
solna=NestList[EMStep,{0,1},4]
:[font = output; output; inactive; preserveAspect; endGroup]
{{0, 1}, {0.1, 1.1}, {0.2, 1.22}, {0.3, 1.364}, 
 
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;[o]
{{0, 1}, {0.1, 1.1}, {0.2, 1.22}, {0.3, 1.364}, 
 
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:[font = input; preserveAspect; startGroup]
pa = ListPlot[solna,PlotStyle->{RGBColor[0,1,0]}]
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Graphics["<<>>"]
;[o]
-Graphics-
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h = 0.05;
:[font = input; preserveAspect; startGroup]
solnb=NestList[EMStep,{0,1},8]
:[font = output; output; inactive; preserveAspect; endGroup]
{{0, 1}, {0.05, 1.05}, {0.1, 1.105}, {0.15, 1.1655}, 
 
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;[o]
{{0, 1}, {0.05, 1.05}, {0.1, 1.105}, {0.15, 1.1655}, 
 
  {0.2, 1.23205}, {0.25, 1.30525}, {0.3, 1.38578}, 
 
  {0.35, 1.47436}, {0.4, 1.57179}}
:[font = input; preserveAspect; startGroup]
pb = ListPlot[solnb,PlotStyle->{RGBColor[0,0,1]}]
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174]
%!
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Graphics["<<>>"]
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h = 0.025;
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solnc=NestList[EMStep,{0,1},16]
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{{0, 1}, {0.025, 1.025}, {0.05, 1.05125}, 
 
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{{0, 1}, {0.025, 1.025}, {0.05, 1.05125}, 
 
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