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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "de:=diff(p(t),t)=alp
ha*p(t);\ninits:=p(1890)=63,p(1970)=203;\nsol:=dsolve(\{de,inits\},\{p
(t),alpha\});\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "de:=diff
(p(t),t)=alpha*p(t);\ninits:=p(1890)=63,p(1970)=203;\nsol:=dsolve(\{de
,inits\},p(t));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "restar
t:de:=diff(p(t),t)=alpha*p(t);\ninits:=p(1890)=63;\nsol:=dsolve(\{de,i
nits\},p(t));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "rsol:=su
bs(t=1970,rhs(sol));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sol
ve(rsol=203,alpha);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "p. 114 #9" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "g:=981/100:d9:=diff(v(t),
t)*100=(g-1/40)*100-10*v(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 29 "s9:=dsolve(\{d9,v(0)=0\},v(t));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "solve(rhs(s9)=70,t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "evalf(1957/20);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 24 "Improved \+
Euler's method." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 184 "impe:=p
roc(x0, y0, c, N)\n local h,x,y,F,G,i: h:=evalf((c-x0)/N): x:=x0: y:=y
0:\n for i to N do\n  F:=f(x,y):\n  G:=f(x+h,y+h*F):\n  x:=x+h:\n  y:=
y+evalf(h*(F+G)/2): \n od:\n print(x,y);\nend;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "p. 126 #8" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f:=(x,y)->(y^2+x)/x;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "impe(1,1,1.8,400);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "eul:=proc(x0, y0, c, N)\n l
ocal h,x,y,F,i: h:=evalf((c-x0)/N): x:=x0: y:=y0:\n for i to N do\n  F
:=f(x,y):\n  x:=x+h:\n  y:=y+evalf(h*F):\n  print(x,y);\n od:\n print(
x,y);\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eul(1,1,1.8,
4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "[I think the N=8 in the pr
oblem is an error.]  Can we solve the problem exactly:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "restart:d8:=diff(y(x),x)=(y(x)^2+x)
/x; i8:=y(1)=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s8:=dsol
ve(\{d8,i8\},y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eval
f(subs(x=1.8,rhs(s8)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "
n8:=dsolve(\{d8,i8\},y(x),numeric);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "n8(1.8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
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