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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "# Graphing the directionfiel
d of a DE and solving the DE;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 51 "   # 1.We define a differential equation as follows" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "        de:=diff(y(x),x)=y/(1+x^2);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "   # 2.Graphing the dir
ection field" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "        DEp
lot(de,y(x),x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 88 "   # 3. Solving the DE. The  \" _C1 \" stands  for multiplicatio
n by arbitrary constant C1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "        f:=dsolve(de,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 29 "   # 4. Initial value problem" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "        f:=dsolve(\{de,y(0)=5\},y(x));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "   # 5. Lets consider an other ODE:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "        de:=diff(y(x),x
)=x+cos(y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "        d
solve(de,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "   # No \+
answer because the ODE is too hard. We will use numerical methods (Eul
er's method)" }}}}{MARK "13 0 0" 82 }{VIEWOPTS 1 1 0 1 1 1803 }