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" }}{PARA 0 "" 0 "" {TEXT 290 68 "\317 \356 \354\345\362\356\344\350\352\345 z(x) \355\340\365\356\344\350\3 54 \350\347 \360\345\370\345\355\350\377 \352\360\340\345\342\356\351 \+ \347\340\344\340\367\350 \361\353\345\344\363\376\371\345\343\356 \342 \350\344\340:" }}{PARA 0 "" 0 "" {TEXT 290 0 "" }}{PARA 0 "" 0 "" {TEXT 290 32 " . \307\344\345\361\374 s1 \350 s2 - \352\356\355\361 \362\340\355\362\373." }}{PARA 0 "" 0 "" {TEXT 290 0 "" }}{PARA 0 "" 0 "" {TEXT 290 82 "\324\363\355\352\366\350\376 w(x,t) \356\357\360\345 \344\345\353\377\345\354 \352\340\352 \357\356\352\340\347\340\355\356 \342 \364\340\351\353\345: \"...\312\356\354\357\322\345\365\355\\Map le\\\323\314\324\\\320\345\370\303\350\357\323\360_W\"" }}{PARA 0 "" 0 "" {TEXT 290 14 "\313\345\352\366\350\377 \271 ____" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 76 "\315\350\346\345 \360\345\352\342\350\34 7\350\362\373, \356\362\354\345\367\345\355\355\373\345 \347\342\345\3 47\344\356\367\352\356\351 *), \355\345\356\341\365\356\344\350\354\35 6 \347\340\344\340\362\374 \361\340\354\356\361\362\356\377\362\345\35 3\374\355\356. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "restart; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 24 "\304\340\355\356 (\302\340 \360 \271 16 \350\347 \320\312 2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "s1:=-1: s2:=0: L:=Pi/2: a:=1: g:=x->cos(x)-x*sin(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arrowG F%F%,&-I$cosGF%6#9$\"\"\"*&F-F.-I$sinGF%F,F.!\"\"F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 44 "\323\352\340\346\345\354 \355\340\367\34 0\353\374\355\373\345 \363\361\353\356\342\350\377 \344\353\377 \364\3 63\355\352\366\350\350 u(x,t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=x->-cos(x); F:=x->0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I \"xG6\"F%6$I)operatorGF%I&arrowGF%F%,$-I$cosGF%6#9$!\"\"F%F%F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arrowGF%F %\"\"!F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 46 "\322\340\352\350 \354 \356\341\360\340\347\356\354, \360\345\370\340\345\354 \361\353\3 45\344\363\376\371\363\376 \352\360\340\345\342\363\376 \347\340\344\3 40\367\363" }{TEXT 290 2 " " }{TEXT 213 18 "\361\356 \361\362\340\366 \350\356\355\340\360\355\373\354\350 \n" }{TEXT 214 17 "\355\345\356\3 44\355\356\360\356\344\355\356\361\362\377\354\350:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "deu:=diff(u(x,t),t$2)=a^2*diff(u(x,t),x$2) +g(x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "/-I%diffG%*protectedG6$-F$6$- I\"uG6\"6$I\"xGF+I\"tGF+F.F.,(-F$6$-F$6$F)F-F-\"\"\"-I$cosG6$F%I(_sysl ibGF+6#F-F4*&F-F4-I$sinGF7F9F4!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 25 "\350\354\345\376\371\363\376 \355\340\367\340\353\374\355\373 \345 \363\361\353\356\342\350\377" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "u(x,0)=f(x); D[2](u)(x,0)=F(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "/-I\"uG6\"6$I\"xGF%\"\"!,$-I$cosG6$%*protectedGI(_syslibG F%6#F'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "/--&I\"DG6$%*protectedGI( _syslibG6\"6#\"\"#6#I\"uGF*6$I\"xGF*\"\"!F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 11 "\350 \343\360\340\355\350\367\355\373\345" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "u(0,t)=s1;u(L,t)=s2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "/-I\"uG6\"6$\"\"!I\"tGF%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "/-I\"uG6\"6$,$I#PiG%*protectedG#\"\"\"\"\"#I\"tGF%\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 64 "\320\345\370\345\355\350\345 \+ \355\340\367\350\355\340\345\354 \361 \356\357\360\345\344\345\353\345 \355\350\377 z(x). \304\353\377 \375\362\356\343\356 \347\340\357\350 \370\345\354 \363\360\340\342\355\345\355\350\345" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 28 "de:=a^2*diff(z(x),x$2)+g(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(-I%diffG%*protectedG6$-F$6$-I\"zG6\"6#I\"xGF+F-F- \"\"\"-I$cosG6$F%I(_syslibGF+F,F.*&F-F.-I$sinGF1F,F.!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 55 "\350 \344\353\377 \355\345\343\356 \343 \360\340\355\350\367\355\373\345 \363\361\353\356\342\350\377 \362\340 \352\350\345 \346\345 \352\340\352 \350 \344\353\377 u(x,t):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "yx0:=z(0)=s1,z(L)=s2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$/-I\"zG6\"6#\"\"!!\"\"/-F%6#,$I#PiG%*p rotectedG#\"\"\"\"\"#F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 31 "\315 \340\365\356\344\350\354 \360\345\370\345\355\350\345 \352\360\340\345 \342\356\351 \347\340\344\340\367\350 " }{TEXT 215 2 "de" }{TEXT 290 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Z:=dsolve(\{de,yx0 \},z(x)); rz:=x->rhs(Z): rz(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "/-I\" zG6\"6#I\"xGF%,(-I$cosG6$%*protectedGI(_syslibGF%F&!\"\"*&F'\"\"\"-I$s inGF+F&F0F.F'F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(-I$cosG6$%*protecte dGI(_syslibG6\"6#I\"xGF(!\"\"*&F*\"\"\"-I$sinGF%F)F-F+F*F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 37 "\321\344\345\353\340\345\354 \357\360\35 6\342\345\360\352\363 \357\356\353\363\367\345\355\355\356\343\356 \36 0\345\370\345\355\350\377 " }{TEXT 216 2 "rz" }{TEXT 290 1 "(" }{TEXT 217 1 "x" }{TEXT 290 43 "), \342 \362\356\354 \367\350\361\353\345 \3 50 \355\340 \363\344\356\342\353\345\362\342\356\360\345\355\350\345 \+ \352\360\340\345\342\373\354" }}{PARA 0 "" 0 "" {TEXT 290 9 "\363\361 \353\356\342\350\377\354:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "odetest(Z, [de, yx0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"\"!F#F #" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 63 "\317\360\350\361\362\363\35 7\340\345\354 \352 \355\340\365\356\346\344\345\355\350\376 \352\356\3 54\357\356\355\345\355\362\373 w(x,t) \352\340\352 \363\352\340\347\34 0\355\356 \342 \364\340\351\353\345: " }}{PARA 0 "" 0 "" {TEXT 290 68 "\"...\312\356\354\357\322\345\365\355\\Maple\\\323\314\324\\\320\345 \370\303\350\357\323\360_W.mws\", \347\340\357\350\361\373\342\340\377 \344\353\377 \355\345\270 \363\360\340\342\355\345\355\350\345:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "dew:=a^2*diff(w(x,t),x$2)-di ff(w(x,t),t$2)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "/,&-I%diffG%*protec tedG6$-F%6$-I\"wG6\"6$I\"xGF,I\"tGF,F.F.\"\"\"-F%6$-F%6$F*F/F/!\"\"\" \"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 18 "\355\340\367\340\353\374 \355\373\345 \363\361\353\356\342\350\377 " }}{PARA 0 "" 0 "" {TEXT 290 1 " " }}{PARA 0 "" 0 "" {TEXT 290 44 "\350 \343\360\340\355\350\36 7\355\373\345 (\355\363\353\345\342\373\345 \357\356 \356\357\360\345 \344\345\353\345\355\350\376) \363\361\353\356\342\350\377" }}{PARA 0 "" 0 "" {TEXT 290 1 " " }{TEXT 290 3 " ." }}{PARA 0 "" 0 "" {TEXT 290 21 "\322\340\352\350\354 \356\341\360\340\347\356\354, \350\354\34 5\345\354 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f1:=x->f(x)-r z(x): F1:=x->F(x): f1(x); F1(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*& I\"xG6\"\"\"\"-I$sinG6$%*protectedGI(_syslibGF%6#F$F&F&F$!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 59 " \302\342\345\344\345\354 \356\341\356\347\355\340\367\345\355 \350\377 \344\353\377 \347\340\357\350\361\350 \361\356\341\361\362\34 2\345\355\355\373\365 \367\350\361\345\353 \350 \364\363\355\352\366\3 50\351:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "omegan:=Pi*n*a/L : N:=infinity:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 218 20 "\307\340\357\3 50\370\345\354 \352\356\354\357\356\355\345\355\362\363 " }{TEXT 219 1 "W" }{TEXT 220 1 "(" }{TEXT 221 1 "x" }{TEXT 222 1 "," }{TEXT 223 1 "t" }{TEXT 224 10 ") \360\345\370\345\355\350\377 " }{TEXT 225 1 "u" } {TEXT 226 1 "(" }{TEXT 227 1 "x" }{TEXT 228 1 "," }{TEXT 229 1 "t" } {TEXT 230 1 ")" }{TEXT 290 2 ". " }}{PARA 0 "" 0 "" {TEXT 290 45 "\315 \340\367\355\345\354 \361 \342\373\367\350\361\353\345\355\350\377 \35 2\356\375\364\364\350\366\350\345\355\362\356\342 \360\377\344\340 \32 4\363\360\374\345:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 64 "- \347\340 \357\350\370\345\354 \352\356\375\364\364\350\366\350\345\355\362\373 \+ \360\377\344\340 \324\363\360\374\345 \344\353\377 \364\363\355\352\36 6\350\351 \355\340\367\340\353\374\355\373\365 \363\361\353\356\342\35 0\351:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "A:=n->2/L*int(f1( x)*sin(Pi*n*x/L), x=0..L); A(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6# I\"nG6\"F%6$I)operatorGF%I&arrowGF%F%,$*&I\"LGF%!\"\"-I$intG6$%*protec tedGI(_syslibGF%6$*&-I#f1GF%6#I\"xGF%\"\"\"-I$sinGF/6#**I#PiGF0F89$F8F 7F8F+F,F8/F7;\"\"!F+F8\"\"#F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$* *I#PiG%*protectedG!\"\",,*$I\"nG6\"\"\"$\"#;*(-I$cosG6$F%I(_syslibGF*6 #*&F$\"\"\"F)F4F4F)F+F$F4\"\"%*&-I$sinGF0F2F4F)\"\"#!#7*(F.F4F)F4F$F4F &F7F4F4F)!\"#,(*$F)F5F,*$F)F9!\")F4F4F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 64 "\310\361\365\356\344\377 \350\347 \361\342\356\351\361\3 62\342 cos(Pi*n) \350 sin(Pi*n), \357\360\356\342\345\344\345\354 \363 \357\360\356\371\345\355\350\345 A(n)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "A(n):=subs(cos(Pi*n)=(-1)^n,sin(Pi*n)=0,A(n)); " }} {PARA 11 "" 1 "" {XPPMATH 20 ",$**I#PiG%*protectedG!\"\",(*$I\"nG6\"\" \"$\"#;*()F&F)\"\"\"F)F+F$F/\"\"%*(F.F/F)F/F$F/F&F/F)!\"#,(*$F)F0F,*$F )\"\"#!\")F/F/F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 80 "*) \317\35 6\353\363\367\345\355\355\373\351 \360\345\347\363\353\374\362\340\362 \361\353\345\344\363\345\362 \357\360\356\340\355\340\353\350\347\350 \360\356\342\340\362\374 \355\340 \355\340\353\350\367\350\345 \356\36 1\356\341\373\365 \362\356\367\345\352 (\362\356\367\345\352 " }} {PARA 0 "" 0 "" {TEXT 290 28 "\360\340\347\360\373\342\340 \350 \344\3 45\353\345\355\350\377 \355\340 \355\356\353\374). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(16*n^4-8*n^2+1=0,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&#!\"\"\"\"#F##\"\"\"F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "singular(16*n^4-8*n^2+1, n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<#/I\"nG6\"I)infinityG%*protectedG<#/F%,$F'!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 231 5 "\302\373\342\356\344" }{TEXT 290 73 ": \342\342\350\344\363 \366\345\353\356\367\350\361\353\345\355\35 5\356\361\362\350 n, - \356\361\356\341\373\365 \362\356\367\345\352 \+ \355\345\362. \302\373\367\350\361\353\377\362\374 \357\360\345\344\3 45\353 \355\345 \355\340\344\356." }}{PARA 0 "" 0 "" {TEXT 290 90 "*) \+ \342 \357\360\356\362\350\342\355\356\354 \361\353\363\367\340\345 A(n ) \361\353\345\344\363\345\362 \357\345\360\345\356\357\360\345\344\34 5\353\350\362\374 (\345\361\353\350 \375\362\356\343\356 \355\345 \361 \344\345\353\340\362\374, \360\345\347\363\353\374\362\340\362 \341\36 3\344\345\362 " }}{PARA 0 "" 0 "" {TEXT 290 39 "\355\345\342\345\360\3 55\373\354 ), \355\340\357\360\350\354\345\360, \350\361\357\356\353\3 74\347\363\377 \356\357\366\350\376 (" }{TEXT 232 10 "substitute" } {TEXT 208 12 ", \361\354. \342\340\360. 9" }{TEXT 290 2 ")." }}} {EXCHG {PARA 0 "" 0 "" {TEXT 290 68 "\316\344\355\340\352\356, \347\34 4\345\361\374 \361\353\345\344\363\345\362 \357\345\360\345\351\362\35 0 \352 \344\350\361\352\360\345\362\355\373\354 \347\355\340\367\345\3 55\350\377\354 A(n) -> Ar[n]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "NN:=40:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for j fro m 1 to NN do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Ar[j]:=A(j)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Ar[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&I#PiG%*pro tectedG!\"\",&#!\")\"$D#\"\"\"F$#F&\"$?\"F+\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 26 "\317\356\353\363\367\350\354 \342\373\360\340\346 \345\355\350\345 \344\353\377 Bn:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "B:=n->2/(Pi*n*a)*int(F1(x)*sin(Pi*n*x/L), x=0..L); B( n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"nG6\"F%6$I)operatorGF%I&ar rowGF%F%,$**I#PiG%*protectedG!\"\"9$F-I\"aGF%F--I$intG6$F,I(_syslibGF% 6$*&-I#F1GF%6#I\"xGF%\"\"\"-I$sinGF26#**F+F:F.F:F9F:I\"LGF%F-F:/F9;\" \"!F?F:\"\"#F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 36 "\322\345\357\345\360\374 \347\340\357\35 0\370\345\354 \342\373\360\340\346\345\355\350\345 \352\356\354\357\35 6\355\345\355\362\373 " }{TEXT 233 1 "W" }{TEXT 290 1 "(" }{TEXT 234 1 "x" }{TEXT 290 1 "," }{TEXT 235 1 "t" }{TEXT 290 16 ") \342 \356\341 \371\345\354 \342\350\344\345: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "W:=(x,t)->sum(Ar[n]*cos(omegan*t)*sin(Pi*n*x/L), n=1..Nn)+sum (B(n)*sin(omegan*t)*sin(Pi*n*x/L), n=1..Nn); W(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"xG6\"I\"tGF%F%6$I)operatorGF%I&arrowGF%F%,&-I$s umG6$%*protectedGI(_syslibGF%6$*(&I#ArGF%6#I\"nGF%\"\"\"-I$cosGF-6#*&I 'omeganGF%F69%F6F6-I$sinGF-6#**I#PiGF.F6F5F69$F6I\"LGF%!\"\"F6/F5;F6I# NnGF%F6-F,6$*(-I\"BGF%F4F6-F>F9F6F=F6FEF6F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I$sumG6$%*protectedGI(_syslibG6\"6$*(&I#ArGF'6#I\"nGF'\" \"\"-I$cosGF$6#,$*&F-F.I\"tGF'F.\"\"#F.-I$sinGF$6#,$*&F-F.I\"xGF'F.F5F ./F-;F.I#NnGF'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 55 "\307\340\357\350\370\345\354 \356\352\35 6\355\367\340\362\345\353\374\355\373\351 \356\362\342\345\362 \342 \3 42\350\344\345 u(x,t)=z(x)+w(x,t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "u:=(x,t)->rz(x)+W(x,t): u(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*-I$cosG6$%*protectedGI(_syslibG6\"6#I\"xGF(!\"\"*&F*\" \"\"-I$sinGF%F)F-F+F*F--I$sumGF%6$*(&I#ArGF(6#I\"nGF(F--F$6#,$*&F7F-I \"tGF(F-\"\"#F--F/6#,$*&F7F-F*F-F=F-/F7;F-I#NnGF(F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 49 "\352\356\362\356\360\373\351 \344\356\353\346\3 45\355 \363\344\356\342\353\345\362\342\356\360\377\362\374 \350\361\3 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