{VERSION 2 3 "IBM INTEL NT" "2.3" }
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "#p3=v(x)*p1+w(x)*u   The initial OD
E\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "#The complete deriv
ative operator restricted to the ODE\nFD:=(ff)->diff(ff,x) + p1*diff(f
f,u) + p2*diff(ff,p1) + (v(x)*p1+w(x)*u)*diff(ff,p2);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#FDG:6#%#ffG6\"6$%)operatorG%&arrowGF(,*-%%diffG
6$9$%\"xG\"\"\"*&%#p1GF2-F.6$F0%\"uGF2F2*&%#p2GF2-F.6$F0F4F2F2*&,&*&-%
\"vG6#F1F2F4F2F2*&-%\"wGFAF2F7F2F2F2-F.6$F0F9F2F2F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 173 "# The k-power of FD.\nFDK:=proc (f
,k) \n  local pp,i; \n  pp:=f;\n\011 if k>0 then \n    for i from 1 by
 1 to k do\n             pp:=FD(pp);\n             od;\n  fi;\n  RETUR
N(pp);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "# The unive
rsal linearisation operator.\nl:=(g)->FDK(g,3)-v(x)*FDK(g,1)-w(x)*g; \+
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG:6#%\"gG6\"6$%)operatorG%&ar
rowGF(,(-%$FDKG6$9$\"\"$\"\"\"*&-%\"vG6#%\"xGF2-F.6$F0F2F2!\"\"*&-%\"w
GF6F2F0F2F:F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "#G:=g(x,
u,p1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "l1:=l(g(x,u,p1));
" }}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "collect(l1,p2);" }}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "#g:=a(x,u)*p1^2+b(x,u)*p1+c(
x,y);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#l2:=l(g);" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "#collect(l2,[p2,p1]);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0" 14 }{VIEWOPTS 1 1 0 1 1 1803 
}