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00000000000000000000000000000000000000000}}{INP_R 49 0 "> "{TEXT 0 29 "r:=diff(y(t),t)=1/2-t+2*y(t);"}}{OUT_R 50 0 49{DAG :3n3\`r` =3(3n4\`diff`,3(3n3\`y`,2n3\`t`pD+7/3j2x0001j2x0002p12pDi2x0001p9 p14}}{INP_R 51 0 "> "{TEXT 0 13 "z:=diff(r,t);"}}{OUT_R 52 0 51 {DAG :3n3\`z`=3(3n4\`diff`,3(3p5,3(3n3\`y`,2n3\`t`p10p10+5i2x0001 j2x0001p9j2x0002}}{INP_R 53 0 "> "{TEXT 0 23 "secder:=subs(r,rhs( z));"}}{OUT_R 54 0 53{DAG :3n4\`secder`+5n3\`t`i2x0002(3n3\`y`,2p 5j2x0004}}{INP_R 55 0 "> "{TEXT 0 19 "En_1:=secder*h^2/2;"}} {OUT_R 56 0 55{DAG :3n4\`En_1`+3*5+5n3\`t`i2x0002(3n3\`y`,2p7j2x0 004j2x0001n3\`h`j2x0002/3p12p16}}{INP_R 57 0 "> "{TEXT 0 21 "en_1 :=subs(sol,En_1);"}}{OUT_R 58 0 57{DAG :3n4\`en_1`+3*5(3n3\`exp`, 2+3n3\`t`j2x0002j2x0001n3\`h`pDpD}}{INP_R 59 0 "> "{TEXT 0 39 "e1 :=subs((h=.1,t=.1),en_1); evalf(\");"}}{OUT_R 60 0 59{DAG :3n3\ `e1`+3(3n3\`exp`,2e3j2x0002i2x0001e3p9i2x0002}}{OUT_R 61 0 59{DAG e3j4x002442805516i2x0011}}{INP_R 62 0 "> "{TEXT 0 39 "e4:=subs(( h=.1,t=.4),en_1); evalf(\");"}}{OUT_R 63 0 62{DAG :3n3\`e4`+3(3 n3\`exp`,2e3j2x0008i2x0001e3j2x0002i2x0002}}{OUT_R 64 0 62{DAG e3 j4x004451081856i2x0011}}{SEP_R 65 0}{COM_R 66 0{TEXT 1 50 "Here i s the second problem (number 4 on each page)"}}{INP_R 67 0 "> " {TEXT 0 0 ""}}{INP_R 68 0 "> "{TEXT 0 40 "diffeq2:=diff(ny(t),t)= 5*t-3*(ny)^(1/2);"}}{OUT_R 69 0 68{DAG :3n4\`diffeq2`=3(3n4\`diff `,3(3n3\`ny`,2n3\`t`pE+5pEj2x0005*3pB/3j2x0001j2x0002i2x0003}} {INP_R 70 0 "> "{TEXT 0 38 "y0:=(ny,h,t)->ny+h*(5*t-3*(ny)^(1/2)) ;"}}{OUT_R 71 0 70{DAG :3n3\`y0`@8,4n3\`ny`n3\`h`n3\`t`,1,3n5\`op erator`n4\`arrow`pB+5a2x0001j2x0001*5a2x0002p18+5a2x0003j2x0005*3 p16/3p18j2x0002i2x0003p18p18pBpB}}{INP_R 72 0 "> "{TEXT 0 26 "y0( 1,.1,0); y1:=evalf(\");"}}{OUT_R 73 0 72{DAG e3j2x0007i2x0001}} {OUT_R 74 0 72{DAG :3n3\`y1`e3j2x0007i2x0001}}{INP_R 75 0 "> " {TEXT 0 17 "y2:=y0(y1,.1,.1);"}}{OUT_R 76 0 75{DAG :3n3\`y2`e3j4x 004990019920i2x0010}}{INP_R 77 0 "> "{TEXT 0 17 "y3:=y0(y2,.1,.2) ;"}}{OUT_R 78 0 77{DAG :3n3\`y3`e3j4x003870817728i2x0010}}{INP_R 79 0 "> "{TEXT 0 17 "y4:=y0(y3,.1,.3);"}}{OUT_R 80 0 79{DAG :3n3\ `y4`e3j4x003504340845i2x0010}}{INP_R 81 0 "> "{TEXT 0 16 "y1:=y0( 1,.05,0);"}}{OUT_R 82 0 81{DAG :3n3\`y1`e3j2x0085i2x0002}}{INP_R 83 0 "> "{TEXT 0 18 "y2:=y0(y1,.05,.1);"}}{OUT_R 84 0 83{DAG :3n3 \`y2`e3j4x007367068331i2x0010}}{INP_R 85 0 "> "{TEXT 0 18 "y3:=y0 (y2,.05,.2);"}}{OUT_R 86 0 85{DAG :3n3\`y3`e3j4x006579593914i2x00 10}}{INP_R 87 0 "> "{TEXT 0 18 "y4:=y0(y3,.05,.3);"}}{OUT_R 88 0 87{DAG :3n3\`y4`e3j4x006112873474i2x0010}}{INP_R 89 0 "> "{TEXT 0 17 "y1:=y0(1,.025,0);"}}{OUT_R 90 0 89{DAG :3n3\`y1`e3j2x0925i2x 0003}}{INP_R 91 0 "> "{TEXT 0 19 "y2:=y0(y1,.025,.1);"}}{OUT_R 92 0 91{DAG :3n3\`y2`e3j4x008653673098i2x0010}}{INP_R 93 0 "> " {TEXT 0 19 "y3:=y0(y2,.025,.2);"}}{OUT_R 94 0 93{DAG :3n3\`y3`e3j 4x008205984692i2x0010}}{INP_R 95 0 "> "{TEXT 0 19 "y4:=y0(y3,.025 ,.3);"}}{OUT_R 96 0 95{DAG :3n3\`y4`e3j4x007901583015i2x0010}} {INP_R 97 0 "> "{TEXT 0 16 "inits2:=ny(0)=2;"}}{OUT_R 98 0 97{DAG :3n4\`inits2`=3(3n3\`ny`,2j2x0000j2x0002}}{INP_R 99 0 "> "{TEXT 0 37 "sol2:=dsolve(\{diffeq2,inits2\},ny(t));"}}{OUT_R 100 0 99 {DAG :3n4\`sol2`,1}}{COM_R 101 0{TEXT 1 127 "The solution is noth ing because maple cannot solve it explicitly, so we are going to \+ leave the actual solution out of the plot."}}{INP_R 102 0 "> " {TEXT 0 0 ""}}{INP_R 103 0 "> "{TEXT 0 107 "p2:=DEplot(diff(y(t), t)=5*t-3*(y(t))^(1/2),[t,y],0..0.4,\{[0,1]\}, stepsize=.1, method ='Euler', thickness=1):"}}{INP_R 104 0 "> "{TEXT 0 108 "p3:=DEplo t(diff(y(t),t)=5*t-3*(y(t))^(1/2),[t,y],0..0.4,\{[0,1]\}, stepsiz e=.05, method='Euler', thickness=2):"}}{INP_R 105 0 "> "{TEXT 0 109 "p4:=DEplot(diff(y(t),t)=5*t-3*(y(t))^(1/2),[t,y],0..0.4,\{[0 ,1]\}, stepsize=.025, method='Euler', thickness=3):"}}{INP_R 106 0 "> "{TEXT 0 20 "display([p2,p3,p4]);"}}{GRH_R 107 0{RASTER 500 427 1 63 00000000000000001800000000000000000000000000000000000000 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