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0 "> "{TEXT 0 29 "with(DEtools): with(plots):  "}}{SEP_R 3 0}
{COM_R 4 0{TEXT 1 0 ""}}{INP_R 5 0 "> "{TEXT 0 95 "p1:=DEplot(dif
f(y(x),x)=3*y(x)+1,[x,y],0..0.5,\{[0,.1]\},stepsize=.1,method=`Eu
ler`,thickness=1):"}}{SEP_R 6 0}{COM_R 7 0{TEXT 1 0 ""}}{INP_R 8 
0 "> "{TEXT 0 96 "p2:=DEplot(diff(y(x),x)=3*y(x)+1,[x,y],0..0.5,\
{[0,.1]\},stepsize=.05,method=`Euler`,thickness=2):"}}{SEP_R 9 0}
{INP_R 10 0 "> "{TEXT 0 96 "p3:=DEplot(diff(y(x),x)=3*y(x)+1,[x,y
],0..0.5,\{[0,.1]\},stepsize=.01,method=`Euler`,thickness=3):"}}
{COM_R 11 0{TEXT 1 0 ""}}{INP_R 12 0 "> "{TEXT 0 47 "diffeq1:=dif
f(y(x),x)=3*y(x)+1; inits:=y(0)=.1;"}}{OUT_R 13 0 12{DAG :3n4\`di
ffeq1`=3(3n4\`diff`,3(3n3\`y`,2n3\`x`pE+5pAj2x0003j2x0001p15}}
{OUT_R 14 0 12{DAG :3n4\`inits`=3(3n3\`y`,2j2x0000e3j2x0001i2x000
1}}{INP_R 15 0 "> "{TEXT 0 35 "sol1:=dsolve(\{diffeq1,inits\},y(x
));"}}{OUT_R 16 0 15{DAG :3n4\`sol1`=3(3n3\`y`,2n3\`x`+5/3i2x0001
j2x0003j2x0001(3n3\`exp`,2+3p9pFe3j4x004333333333i2x0010}}{INP_R 
17 0 "> "{TEXT 0 29 "p4:=plot(rhs(sol1),x=0..0.4):"}}{INP_R 18 0 
"> "{TEXT 0 0 ""}}{INP_R 19 0 "> "{TEXT 0 23 "display([p1,p2,p3,p
4]);"}}{COM_R 20 0{TEXT 1 52 "HERE IS THE SAME PROBLEM SOLVED WIT
H IMPROVED EULER:"}}{SEP_R 21 0}{COM_R 22 0{TEXT 1 0 ""}}{INP_R 
23 0 "> "{TEXT 0 98 "p5:=DEplot(diff(y(x),x)=3*y(x)+1,[x,y],0..0.
5,\{[0,.1]\},stepsize=.1,method=`impeuler`,thickness=1):"}}{SEP_R
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plot(diff(y(x),x)=3*y(x)+1,[x,y],0..0.5,\{[0,.1]\},stepsize=.05,m
ethod=`impeuler`,thickness=2):"}}{SEP_R 27 0}{INP_R 28 0 "> "
{TEXT 0 99 "p7:=DEplot(diff(y(x),x)=3*y(x)+1,[x,y],0..0.5,\{[0,.1
]\},stepsize=.01,method=`impeuler`,thickness=3):"}}{INP_R 29 0 ">
 "{TEXT 0 23 "display([p4,p5,p6,p7]);"}}{INP_R 30 0 "> "{TEXT 0 
18 "?DEtools[options];"}}}{END}