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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 32 "Perem\351rt\351k-feladat \+
l\366v\366ld\366z\351ssel" }}{PARA 19 "" 0 "" {TEXT -1 44 "Bartha Fere
nc ir\341ny\355t\341s\341val k\366z\366s \363rai munka" }}{PARA 19 "" 
0 "" {TEXT -1 38 "SZTE, Elm. Fiz. 2003. m\341rcius-\341prilis " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 
1 "restart;with(plots):" "6#C$%(restartG-%%withG6#%&plotsG" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 35 "A megoldand\363 differenci\341legyenlet: \+
" }{XPPEDIT 19 1 "eq:=diff(f(x),x$2)+(f(x))^2=1:\n" "6#>%#eqG/,&-%%dif
fG6$-%\"fG6#%\"xG-%\"$G6$F-\"\"#\"\"\"*$-F+6#F-F1F2F2" }}{PARA 0 "" 0 
"" {TEXT -1 49 "kezdeti\351rt\351k-probl\351mak\351nt integr\341lhat
\363, p\351ld\341ul: " }{XPPEDIT 19 1 "ivp:=f(0)=0,D(f)(0)=1:\n" "6#>%
$ivpG6$/-%\"fG6#\"\"!F*/--%\"DG6#F(6#F*\"\"\"" }}{PARA 0 "" 0 "" 
{TEXT -1 29 "mellett a numerikus megold\341s " }{XPPEDIT 19 1 "isp:=ds
olve(\{eq,ivp\},numeric,range=0..1):odeplot(isp);" "6#C$>%$ispG-%'dsol
veG6%<$%#eqG%$ivpG%(numericG/%&rangeG;\"\"!\"\"\"-%(odeplotG6#F%" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Perem\351rt\351k-probl\351mak\351n
t a feladat \366sszetett. Keress\374k olyan megold\341st, hogy " }
{XPPEDIT 19 1 "f(0)=0:" "6#/-%\"fG6#\"\"!F'" }{TEXT -1 4 " \351s " }
{XPPEDIT 19 1 "f(1)=0:" "6#/-%\"fG6#\"\"\"\"\"!" }{TEXT -1 8 " legyen!
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Els\365 pr\363b\341lkoz\341s \+
IVP-re :\n" }{MPLTEXT 1 0 65 "ivp:=f(0)=0,D(f)(0)=1:\nisp:=dsolve(\{eq
,ivp\},numeric,range=0..1):\n" }{TEXT -1 39 "Menteni a biztosan nem j
\363 eredm\351nyt...." }{MPLTEXT 1 0 73 "\npl[1]:=odeplot(isp):uold:=s
ubs(isp(1),f(x)):print(`f(1)`=uold):vold:=1:\n" }{TEXT -1 23 "\311s m
\341sikat pr\363b\341lni...." }{MPLTEXT 1 0 8 "vnew:=0:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "i:=1:u:=1:\n" }{TEXT -1 37 "Ciklusb
an, Newton-extrapol\341ci\363val...." }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 217 "while (abs(u)>10^(-8)) do\nv:=vnew:\nivp:=f(0)=0,D(f)(0)=v:\nis
p:=dsolve(\{eq,ivp\},numeric,range=0..1):i:=i+1:pl[i]:=odeplot(isp):\n
uold:=u:\nu:=subs(isp(1),f(x)):print(`f(1)`=u);\nvnew:=v-u/((u-uold)/(
v-vold)):\nvold:=v:\nod:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Az er
edm\351ny: " }{MPLTEXT 1 0 15 "display(pl[i]);" }}}{EXCHG {PARA 0 "" 
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