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"" {MPLTEXT 1 0 30 "D[2](u)(x, 0): convert(%,diff):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 502 10 "\317\360 \350\354\345\367\340\355\350\345" }{TEXT -1 69 ". \307\344\345\361\374 \354\373 \341\363\344\345\354 \343\356\342\356\360\350\362\374 \362 \356\353\374\352\356 \356 \362\360\345\365 \362\350\357\340\365 \343 \360\340\355\350\367\355\373\365 \363\361\353\356\342\350\351 [19]:" } }{PARA 0 "" 0 "" {TEXT -1 32 "- \343\360\340\355\350\367\355\373\345 \+ \363\361\353\356\342\350\377 1-\343\356 \360\356\344\340: " }{TEXT 503 1 "u" }{TEXT -1 3 "(0," }{TEXT 504 1 "t" }{TEXT -1 2 ")=" }{TEXT 510 3 "phi" }{TEXT -1 1 "(" }{TEXT 505 1 "t" }{TEXT -1 4 "); " } {TEXT 506 1 "u" }{TEXT -1 1 "(" }{TEXT 507 1 "L" }{TEXT -1 1 "," } {TEXT 508 1 "t" }{TEXT -1 2 ")=" }{TEXT 511 3 "psi" }{TEXT -1 1 "(" } {TEXT 509 1 "t" }{TEXT -1 2 ");" }}{PARA 0 "" 0 "" {TEXT -1 32 "- \343 \360\340\355\350\367\355\373\345 \363\361\353\356\342\350\377 2-\343 \356 \360\356\344\340: " }{TEXT 512 1 "D" }{TEXT -1 4 "[1](" }{TEXT 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\"LGF.F-!\"\"F.F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGf*6#%\" xG6\"6$%)operatorG%&arrowGF(\"\"!F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "- \364\363\355\352\366\350\350 " }{TEXT 544 3 "phi" } {TEXT -1 1 "(" }{TEXT 542 1 "t" }{TEXT -1 5 ") \350 " }{TEXT 545 3 "p si" }{TEXT -1 1 "(" }{TEXT 543 1 "t" }{TEXT -1 51 "), \347\340\344\340 \376\371\350\345 \357\360\340\342\373\345 \367\340\361\362\350 \343 \360\340\355\350\367\355\373\365 \363\361\353\356\342\350\351 \360\345 \370\345\355\350\377 " }{TEXT 539 1 "u" }{TEXT -1 1 "(" }{TEXT 541 1 " x" }{TEXT -1 1 "," }{TEXT 540 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "phi:=t->1-cos(t); psi:=t->0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phiGf*6#%\"tG6\"6$%)operatorG%&arrowGF(,& \"\"\"F--%$cosG6#9$!\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$p siGf*6#%\"tG6\"6$%)operatorG%&arrowGF(\"\"!F(F(F(" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 83 "*) \317\356\361\353\345\344\355\345\345 \356\362 \360\340\347\350\354 \342 \342\350\344\345 \367\345\362\373\360\345 \365 \360\340\342\345\355\361\362\342, \352\356\362\356\360\373\345 \+ \347\340\357\350\361\340\355\373 \355\350\346\345. \315\363\346\355 \356\345 \350\347 \355\350\365 " }}{PARA 0 "" 0 "" {TEXT -1 32 "\361 \353\345\344\363\345\362 \356\362\352\360\373\362\374, \361\355\377 \342 \340\357\356\361\362\360\356\364\373." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 49 "u(0,t):=phi(t); u(L,t):=psi(t); " }{TEXT -1 2 "1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"uG6$\"\"!%\"tG ,&\"\"\"F*-%$cosG6#F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"uG6 $\"\"\"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "`D[1]( u)(0,t):=phi(t); D[1](u)(L,t):=psi(t);`: " }{TEXT -1 2 "2)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "`D[1](u)(0,t):=phi(t); u(L,t ):=psi(t);`: " }{TEXT -1 2 "3)" }{MPLTEXT 1 0 4 " " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "`u(0,t):=phi(t); D[1](u)(L,t ):=psi(t);`: " }{TEXT -1 17 " 4)" }{MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "" 0 "" 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"u" } {TEXT -1 1 "(" }{TEXT 560 1 "x" }{TEXT -1 1 "," }{TEXT 561 1 "t" } {TEXT -1 26 ") \361\356\342\357\340\344\340\353\350 \361\356 \347\355 \340\367\345\355\350\377\354\350 " }{TEXT 563 1 "z" }{TEXT -1 1 "(" } {TEXT 562 1 "x" }{TEXT -1 1 "," }{TEXT 564 1 "t" }{TEXT -1 26 ") \342 \+ \340\355\340\353\356\343\350\367\355\373\365 \362\356\367\352\340\365, \362\356" }}{PARA 0 "" 0 "" {TEXT -1 32 "\345\361\362\374 \350\365 \+ \360\340\347\355\356\361\362\374 \360\340\342\355\377\353\340\361\374 \+ \355\363\353\376." }}{PARA 0 "" 0 "" {TEXT -1 82 "\321\364\356\360\354 \350\360\363\345\354 \353\356\343\350\367\345\361\352\350\351 \341\353 \356\352 \342\373\341\356\360\340 \362\350\357\340 \343\360\340\355 \350\367\355\373\365 \363\361\353\356\342\350\351, \352\356\362\356 \360\373\345 \341\363\344\363\362 \356\357\360\345\344\345\353\377\362 \374" }}{PARA 0 "" 0 "" {TEXT -1 46 "(\347\340\344\340\367\340 \330 \362\363\360\354\340-\313\350\363\342\350\353\353\377) \361\356\341 \361\362\342\345\355\355\373\345 \347\355\340\367\345\355\350\377 " } {TEXT 548 1 "b" }{TEXT -1 1 "(" }{TEXT 549 1 "n" }{TEXT -1 24 ") \350 \+ \361\356\341\361\362\342\345\355\355\373\345 \364\363\355\352\366\350 \350 " }{TEXT 550 2 "Xn" }{TEXT -1 1 "(" }{TEXT 551 1 "x" }{TEXT -1 1 "," }{TEXT 552 1 "n" }{TEXT -1 3 "), " }}{PARA 0 "" 0 "" {TEXT -1 74 " \340 \362\340\352\346\345 \357\356\344\341\350\360\340\345\354\363\376 \342 \363\352\340\347\340\355\355\356\354 \342\373\370\345 \361\354 \373\361\353\345 \352 \343\360\340\355\350\367\355\373\354 \363\361 \353\356\342\350\377\354 \364\363\355\352\366\350\376 " }{TEXT 553 1 "z" }{TEXT -1 1 "(" }{TEXT 554 1 "x" }{TEXT -1 1 "," }{TEXT 555 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "if u(0,t )=phi(t)and u(L,t)=psi(t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "b :=n->Pi*n/L: Xn:=(x,n)->sin(b(n)*x):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->phi(t)+x/L*(psi(t)-phi(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$% )operatorG%&arrowG6\",&-%$phiG6#F(\"\"\"*(F'F2%\"LG!\"\",&-%$psiG6#F(F 2-F06#F(F5F2F2F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "elif D[1](u )(0,t)=phi(t) and D[1](u)(L,t)=psi(t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "b:=n->Pi*n/L: Xn:=(x,n)->cos(b(n)*x): " }}{PARA 0 "> \+ " 0 "" {XPPEDIT 19 1 "z:=(x,t)->x*phi(t)+x^2/2/L*(psi(t)-phi(t))" "6#> %\"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arrowG6\",&*&F'\"\"\"-%$phiG6#F(F 0F0**F'\"\"#F5!\"\"%\"LGF6,&-%$psiG6#F(F0-F26#F(F6F0F0F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "elif D[1](u)(0,t)=phi(t) and u(L,t)=psi(t ) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "b:=n->Pi*(2*n-1)/2/L: Xn: =(x,n)->cos(b(n)*x):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->x*p hi(t)+(psi(t)-L*phi(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arro wG6\",&*&F'\"\"\"-%$phiG6#F(F0F0,&-%$psiG6#F(F0*&%\"LGF0-F26#F(F0!\"\" F0F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "elif u(0,t)=phi(t) and \+ D[1](u)(L,t)=psi(t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "b:=n->P i*(2*n-1)/2/L: Xn:=(x,n)->sin(b(n)*x):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->phi(t)+x*psi(t)" "6#>%\"zGf*6$%\"xG%\"tG7\"6$%)operato rG%&arrowG6\",&-%$phiG6#F(\"\"\"*&F'F2-%$psiG6#F(F2F2F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "\317\360\356\342\345\344\345\354 \342\350\347\363\340\353\350\347 \340\366\350\376 \342\373\341\360\340\355\355\373\365 \361\356\341\361 \362\342\345\355\355\373\365 \347\355\340\367\345\355\350\351 " } {TEXT 565 1 "b" }{TEXT -1 1 "(" }{TEXT 566 1 "n" }{TEXT -1 23 "), \361 \356\341\361\362\342\345\355\355\373\365 \364\363\355\352\366\350\351 \+ " }}{PARA 0 "" 0 "" {TEXT 567 2 "Xn" }{TEXT -1 1 "(" }{TEXT 568 1 "x" }{TEXT -1 1 "," }{TEXT 569 1 "n" }{TEXT -1 12 ") \350 \364\363\355\352 \366\350\350 " }{TEXT 570 1 "z" }{TEXT -1 1 "(" }{TEXT 571 1 "x" } {TEXT -1 1 "," }{TEXT 572 1 "t" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "b(n);Xn(x,n); z(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%#PiG\"\"\"%\"nGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%$sinG6#*(%#PiG\"\"\"%\"nGF(%\"xGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"\"F$-%$cosG6#%\"tG!\"\"*&%\"xGF$,&F$F)F%F$F$F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "\317\360\356\342\345\360\350\354 \355\340 \356\344\355\356\360\356\344\355\356\361\362\374 \357\356\353\363\367 \345\355\355\373\365 \343\360\340\355\350\367\355\373\365 \363\361\353 \356\342\350\351 \344\353\377 \342\342\356\344\350\354\356\351 \342 \+ \357\356\361\353\345\344\363\376\371\345\354 " }}{PARA 0 "" 0 "" {TEXT -1 61 "\364\363\355\352\366\350\350 W(x,t), \342\373\341\360\340 \342 \355\350\346\345 \355\363\346\355\363\376 \361\362\360\356\367 \352\363 \350 \361\355\377\342 \340\357\356\361\362\360\356\364\373. \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "Ww(x,t): Ww(0,t)=u(0,t) -z(0,t); Ww(L,t)=u(L,t)-z(L,t); " }{TEXT -1 2 "1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"!%\"tGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"\"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "D[1](Ww)(0,t)=D[1](u)(0,t)-D[1](z)(0,t); D[1](Ww)(L,t)=D[1](u) (L,t)-D[1](z)(L,t); " }{TEXT -1 2 "2)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$\"\"!%\"tG,(--F&6#%\"uGF,F)F)F)-%$cosG6#F .!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$F) %\"tG,(--F&6#%\"uGF,F)F)F)-%$cosG6#F-!\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 64 "D[1](Ww)(0,t)=D[1](u)(0,t)-D[1](z)(0,t); Ww(L,t)=u( L,t)-z(L,t); " }{TEXT -1 2 "3)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--& %\"DG6#\"\"\"6#%#WwG6$\"\"!%\"tG,(--F&6#%\"uGF,F)F)F)-%$cosG6#F.!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"\"%\"tG\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "Ww(0,t)=u(0,t)-z(0,t); D[1]( Ww)(L,t)=D[1](u)(L,t)-D[1](z)(L,t); " }{TEXT -1 2 "4)" }{MPLTEXT 1 0 3 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"!%\"tGF'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$F)%\"tG,(--F &6#%\"uGF,F)F)F)-%$cosG6#F-!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 324 12 "\317\360\350\354\345\367\340\355\350\345. " }{TEXT -1 67 "\307\340 \357\350\370\345\354 \344\353\377 1-\351 \352\360\340\345\342\356\351 \+ \347\340\344\340\367\350 \362\340\352 \355\340\347\373\342\340\345\354 \373\345 \363\361\353\356\342\350\377 \361\356\343\353\340\361\356\342 \340\355\350\377:" }{TEXT 331 1 " " }}{PARA 0 "" 0 "" {TEXT 573 1 "u" }{TEXT -1 6 "(0,0)=" }{TEXT 325 1 "f" }{TEXT -1 4 "(0)=" }{TEXT 326 3 "phi" }{TEXT -1 6 "(0) \350 " }{TEXT 327 1 "u" }{TEXT -1 1 "(" }{TEXT 330 1 "L" }{TEXT -1 4 ",0)=" }{TEXT 328 1 "f" }{TEXT -1 1 "(" }{TEXT 332 1 "L" }{TEXT -1 2 ")=" }{TEXT 329 3 "psi" }{TEXT -1 53 "(0), \342 \373\357\356\353\355\345\355\350\345 \352\356\362\356\360\373\365 \355 \345\353\374\347\377 \361\352\340\347\340\362\374 \356\341\377\347\340 \362\345\353\374\355\356\345, " }}{PARA 0 "" 0 "" {TEXT -1 76 "\355 \356 - \346\345\353\340\362\345\353\374\355\356\345. \310\347\354\345 \355\345\355\350\345 \343\360\340\355\350\367\355\373\365 \363\361\353 \356\342\350\351 \350\347\354\345\355\377\345\362 \363\361\353\356\342 \350\377 \361\356\343\353\340\361\356\342\340\355\350\377." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "if f(0)=phi(0) and f(L)=psi(0) then sogL:=`\363\361\353\356\342\350\377 \361\356\343\353\340\361\356\342 \340\355\350\377 \342\373\357\356\353\355\345\355\373` " }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 51 "else sogL:=`\363\361\353\356\342\350\377 \361 \356\343\353\340\361\356\342\340\355\350\377 \355\345 \342\373\357\356 \353\355\345\355\373` fi: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 " \350 \357\360\350\342\345\344\345\354 \342\350\347\363\340\353\350 \347\340\366\350\376 \350\365 \342\373\357\356\353\355\345\355\350\377 \355\340 \344\350\361\357\353\345\345" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "sogL; " }{TEXT -1 6 "\316\362\342\345\362:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?|^z|\\z|fy|iy|]y|cy|jz~|\\z|iy|^y|fy|[y|\\ z|iy|]y|[y|hy|cy|jz~|]y|fz|jy|iy|fy|hy|`y|hy|fzG" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 51 "*) \307\340\344\340\344\350\354 \352\356\355\352 \360\345\362\355\363\376 \364\363\355\352\366\350\376 \342\356\347\354 \363\371\345\355\350\377, \355\340\357\360\350\354\345\360:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g:=(x,t)->sin(x/L); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6$%\"xG%\"tG6\"6$%)operatorG%& arrowGF)-%$sinG6#*&9$\"\"\"%\"LG!\"\"F)F)F)" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 11 "\317\360\350 \375\362\356\354 0<" }{TEXT 284 1 "x" } {TEXT -1 1 "<" }{TEXT 285 1 "L" }{TEXT -1 2 ", " }{TEXT 286 2 " t" } {TEXT -1 66 ">0, \367\362\356 \342\356 \354\355\356\343\356\354 \356 \341\363\361\353\356\342\353\345\355\356 \357\360\345\344\361\362\340 \342\353\345\355\350\345\354 \360\345\370\345\355\350\377 \342 \342 \350\344\345 \360\377\344\340. " }}{PARA 0 "" 0 "" {TEXT -1 80 "\304 \340\353\345\345 \357\356\361\362\360\356\345\355\350\345 \360\345\370 \345\355\350\377 \350\344\345\362 \342 \340\342\362\356\354\340\362 \350\367\345\361\352\356\354 \360\345\346\350\354\345 \342 \361\356 \356\362\342\345\362\361\362\342\350\350 \361 \354\345\362\356\344\350 \352\356\351" }}{PARA 0 "" 0 "" {TEXT -1 82 "\345\343\356 \352\356\354 \357\374\376\362\345\360\355\356\343\356 \350\347\353\356\346\345\355 \350\377 \350 \357\356\347\342\356\353\377\345\362 \342\345\361\362 \350 \344\345\362\340\353\374\355\373\351 \340\355\340\353\350\347, \+ \342 \362\356\354 \367\350\361\353\345 \343\360\340\364\350-" }}{PARA 0 "" 0 "" {TEXT -1 42 "\367\345\361\352\350\351, \352\340\346\344\356 \343\356 \357\360\356\354\345\346\363\362\356\367\355\356\343\356 \360 \345\347\363\353\374\362\340\362\340." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "\320\345\370\345\355\350\345 \350\361\365\356\344\355\356 \343\356 \344\350\364\364\345\360\345\355\366\350\340\353\374\355\356 \343\356 \363\360\340\342\355\345\355\350\377, \363\344\356\342\353 \345\362\342\356\360\377\376\371\345\343\356 \342\373\370\345 \361\364 \356\360\354\363\353\350-" }}{PARA 0 "" 0 "" {TEXT -1 65 "\360\356\342 \340\355\355\373\354 \352\360\340\345\342\373\354 \363\361\353\356\342 \350\377\354, \352\340\352 \341\373\353\356 \361\352\340\347\340\355 \356, \341\363\344\345\354 \350\361\352\340\362\374 \342 \342\350\344 \345 " }}{PARA 0 "" 0 "" {TEXT 440 1 "u" }{TEXT -1 1 "(" }{TEXT 441 1 "x" }{TEXT -1 1 "," }{TEXT 442 1 "t" }{TEXT -1 2 ")=" }{TEXT 443 1 "z " }{TEXT -1 1 "(" }{TEXT 444 1 "x" }{TEXT -1 1 "," }{TEXT 445 1 "t" } {TEXT -1 2 ")+" }{TEXT 451 1 "w" }{TEXT -1 1 "(" }{TEXT 446 1 "x" } {TEXT -1 1 "," }{TEXT 447 1 "t" }{TEXT -1 2 ")+" }{TEXT 448 1 "v" } {TEXT -1 1 "(" }{TEXT 449 1 "x" }{TEXT -1 1 "," }{TEXT 450 1 "t" } {TEXT -1 26 ") \350 \355\340\365\356\344\350\362\374 \350\347 \363\360 \340\342\355\345\355\350\377:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "de:=a^2*diff(u(x,t),x$2)-diff(u(x,t),t$2)+g(x,t)=0:" "6#>%#deG/, (*&%\"aG\"\"#-%%diffG6$-%\"uG6$%\"xG%\"tG-%\"$G6$F0F)\"\"\"F5-F+6$-F.6 $F0F1-F36$F1F)!\"\"-%\"gG6$F0F1F5\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "\304\353\377 \352\340\346\344\356\351 \352\356\354\357 \356\355\345\355\362\373 \360\345\370\345\355\350\377 " }{TEXT 467 1 " u" }{TEXT -1 1 "(" }{TEXT 468 1 "x" }{TEXT -1 1 "," }{TEXT 469 1 "t" } {TEXT -1 9 "), \352\360\356\354\345 " }{TEXT 574 1 "z" }{TEXT -1 1 "( " }{TEXT 575 1 "x" }{TEXT -1 1 "," }{TEXT 576 1 "t" }{TEXT -1 33 "), \+ \347\340\357\350\370\345\354 \361\342\356\270 \344\350\364\364\345\360 \345\355\366\350\340\353\374\355\356\345 " }}{PARA 0 "" 0 "" {TEXT -1 82 "\363\360\340\342\355\345\355\350\345 \361 \367\340\361\362\355\373 \354\350 \357\360\356\350\347\342\356\344\355\373\354\350, \350\347 \+ \352\356\362\356\360\356\343\356 \356\355\340 \344\356\353\346\355\340 \356\357\360\345\344\345\353\377\362\374\361\377, \342 \363\344\356 \341\355\356\354 " }}{PARA 0 "" 0 "" {TEXT -1 50 "\344\353\377 \344 \340\353\374\355\345\351\370\350\365 \342\373\367\350\361\353\345\355 \350\351 \342\350\344\345. \316\344\355\340 \350\347 \352\356\354\357 \356\355\345\355\362 " }{TEXT 428 1 "z" }{TEXT -1 1 "(" }{TEXT 429 1 " x" }{TEXT -1 1 "," }{TEXT 430 1 "t" }{TEXT -1 10 ") \360\345\370\345 \355\350\377 " }{TEXT 431 1 "u" }{TEXT -1 1 "(" }{TEXT 432 1 "x" } {TEXT -1 1 "," }{TEXT 433 1 "t" }{TEXT -1 15 ") \363\346\345 \350\347 \342\345\361\362\355\340 " }}{PARA 0 "" 0 "" {TEXT -1 81 "\350 \345 \270 \347\340\357\350\361\374 \357\360\350\342\356\344\350\362\361\377 \355\350\346\345. \304\342\345 \344\360\363\343\350\345 \341\363\344 \345\354 \350\361\352\340\362\374 \350\347 \357\360\350\342\356\344 \350\354\373\365 \355\350\346\345 \344\350\364\364\345\360\345\355-" } }{PARA 0 "" 0 "" {TEXT -1 31 "\366\350\340\353\374\355\373\365 \363 \360\340\342\355\345\355\350\351. \312\356\354\357\356\355\345\355\362 \363 " }{TEXT 439 1 "w" }{TEXT -1 1 "(" }{TEXT 434 1 "x" }{TEXT -1 1 " ," }{TEXT 435 1 "t" }{TEXT -1 15 ") \350\347 \363\360\340\342\355\345 \355\350\377:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "dew:=a^2*dif f(w(x,t),x$2)-diff(w(x,t),t$2)=0:" "6#>%$dewG/,&*&%\"aG\"\"#-%%diffG6$ -%\"wG6$%\"xG%\"tG-%\"$G6$F0F)\"\"\"F5-F+6$-F.6$F0F1-F36$F1F)!\"\"\"\" !" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "\312\356\354\357\356\355\345 \355\362\363 " }{TEXT 436 1 "v" }{TEXT -1 1 "(" }{TEXT 437 1 "x" } {TEXT -1 1 "," }{TEXT 438 1 "t" }{TEXT -1 29 ") \350\347 \363\360\340 \342\355\345\355\350\377, \344\353\377 \352\356\362\356\360\356\343 \356 " }{TEXT 452 1 "g" }{TEXT -1 2 "1(" }{TEXT 453 1 "x" }{TEXT -1 1 "," }{TEXT 454 1 "t" }{TEXT -1 24 ") \341\363\344\345\362 \356\357\360 \345\344\345\353\345\355\340 \355\350\346\345." }}}{EXCHG {PARA 0 "> \+ " 0 "" {XPPEDIT 19 1 "a^2*diff(v(x,t),x$2)-diff(v(x,t),t$2)+g1(x,t)=0: " "6#/,(*&%\"aG\"\"#-%%diffG6$-%\"vG6$%\"xG%\"tG-%\"$G6$F.F'\"\"\"F3-F 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x=0..L): zg(n,t);" "6#C$>%#zgGf*6$%\"nG%\"tG7\"6$%)operatorG%&arrowG6 \",$*(\"\"#\"\"\"%\"LG!\"\"-%$intG6$*&--&%\"DG6$F1F16#%\"zG6$%\"xGF)F2 -%#XnG6$FAF(F2/FA;\"\"!F3F2F4F.F.F.-F%6$F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#\"\"\"-%$cosG6#%\"tGF&,&*&%#PiGF&%\"nGF&F&-%$s inG6#F,!\"\"F&F-!\"#F.F3F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 " \307\340\357\350\370\345\354 \344\353\377 \357\360\356\342\345\360\352 \350 \357\356\353\363\367\345\355\355\373\351 \342\373\370\345 \360 \345\347\363\353\374\362\340\362, \355\356 \357\356\344 \344\360\363 \343\350\354 \350\354\345\355\345\354 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "gg:=(n,t)->G(n,t)+zg(n,t):gg(n,t);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,&*(\"\"#\"\"\",&**%#PiGF&%\"nGF&-%$cosG6#*&F)F&F*F&F &-%$sinG6#F&F&F&*&-F0F-F&-F,F1F&!\"\"F&,&*&)F)F%F&)F*F%F&F&F&F5F5F5*,F %F&-F,6#%\"tGF&,&F.F&F3F5F&F)!\"#F*F?F5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "\317\360\350" }{TEXT 413 1 " " }{TEXT -1 24 "\375\362\356 \354 \344\356\353\346\355\356 \342\373\357\356\353\355\377\362\374\361 \377:" }{TEXT 407 3 " q" }{TEXT -1 1 "(" }{TEXT 408 1 "n" }{TEXT -1 1 "," }{TEXT 409 1 "t" }{TEXT -1 2 ")=" }{TEXT 410 2 "gg" }{TEXT -1 1 "(" }{TEXT 411 1 "n" }{TEXT -1 1 "," }{TEXT 412 1 "t" }{TEXT -1 29 ") \+ \350 \375\362\356 \354\356\346\345\362 \341\373\362\374 \357\360\356 \342\345\360\352\356\351." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "3.2. \310, \355\340\352\356\355\345\366, \+ \347\340\357\350\370\345\354 \361\340\354\363 3-\376 \352\356\354\357 \356\355\345\355\362\363 " }{TEXT 366 1 "v" }{TEXT -1 1 "(" }{TEXT 367 1 "x" }{TEXT -1 1 "," }{TEXT 368 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "v:=(x,t)->sum((int(q(n,tau)*sin(b(n)* a*(t-tau)), tau=0..t)*Xn(x,n)/(b(n)*a)), n=1..N): simplify(v(x,t));" " 6#C$>%\"vGf*6$%\"xG%\"tG7\"6$%)operatorG%&arrowG6\"-%$sumG6$*(-%$intG6 $*&-%\"qG6$%\"nG%$tauG\"\"\"-%$sinG6#*(-%\"bG6#F:F<%\"aGF<,&F)F " 0 "" {MPLTEXT 1 0 7 "v(0,0); " }}{PARA 11 "" 1 "" 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NN)+sum(- 2*(-cos(Pi*n*t)-cos(Pi*n*t)*(-1)^n*sin(1)+cos(t)+(-1)^n*sin(1))*sin(Pi *n*x)/(Pi^2*n^2-1)/Pi/n,n=1..NN):" "6#C$>%#NNG\"#?>%#UnGf*6$%\"xG%\"tG 7\"6$%)operatorG%&arrowG6\",.\"\"\"F3-%$cosG6#F,!\"\"F+F7*&F+F3-F56#F, F3F3-%$sumG6$,$*.\"\"%F3,&F3F7),$F3F7%\"nGF3F3*$%#PiG\"\"$F7*$FDFGF7-F 56#*(FFF3FDF3F,F3F3-%$sinG6#*(FFF3FDF3F+F3F3F7/FD;F3F%F3-F<6$,$*.\"\"# F3,*-F56#*(FFF3FDF3F,F3F7*(-F56#*(FFF3FDF3F,F3F3),$F3F7FDF3-FM6#F3F3F7 -F56#F,F3*&),$F3F7FDF3-FM6#F3F3F3F3-FM6#*(FFF3FDF3F+F3F3,&*&FFFV*$FDFV F3F3F3F7F7FFF7FDF7F7/FD;F3F%F3F1F1F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "\307\340\354\345\362\350\354, \367\362\356 \347\355\340\367\345 \355\350\345 \375\362\356\343\356 \357\360\345\344\345\353\340 limit( " }{TEXT 481 2 "Un" }{TEXT -1 1 "(" }{TEXT 482 1 "x" }{TEXT -1 1 "," } {TEXT 483 1 "t" }{TEXT -1 3 "), " }{TEXT 480 2 "NN" }{TEXT -1 11 "=inf inity)=" }{TEXT 477 1 "U" }{TEXT -1 1 "(" }{TEXT 478 1 "x" }{TEXT -1 1 "," }{TEXT 479 1 "t" }{TEXT -1 16 ") \360\340\342\355\356 \364\363 \355\352\366\350\350 " }{TEXT 474 1 "U" }{TEXT -1 1 "(" }{TEXT 475 1 " x" }{TEXT -1 1 "," }{TEXT 476 1 "t" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 317 11 "5. \317\360\356\342\345\360\352\340" }{TEXT -1 31 ". \317\356\344\361\362\340\342\350\354 \357\356\353\363\367\345 \355\355\356\345 \360\345\370\345\355\350\345 " }{TEXT 414 1 "U" } {TEXT -1 1 "(" }{TEXT 415 1 "x" }{TEXT -1 1 "," }{TEXT 416 1 "t" } {TEXT -1 36 ") \342 \350\361\365\356\344\355\356\345 \344\350\364\364 \345\360\345\355\366\350\340\353\374\355\356\345 \363\360\340\342-" }} {PARA 0 "" 0 "" {TEXT -1 6 "\355\345\355\350\345 " }{TEXT 256 2 "de" } {TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "re:=subs(u (x,t)=Un(x,t),de): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 3 "5.1" } {TEXT -1 80 ". \302 \357\360\340\342\350\353\374\355\356\361\362\350 \+ \357\356\353\363\367\345\355\355\356\343\356 \360\345\370\345\355\350 \377 \354\356\346\355\356 \363\341\345\344\350\362\374\361\377, \347 \340\357\363\361\362\350\342 \357\360\356\366\345\344\363\360\363 \363 \357\360\356\371\345-" }}{PARA 0 "" 0 "" {TEXT -1 82 "\355\350\377, \+ \342 \360\345\347\363\353\374\362\340\362\345 \352\356\362\356\360\356 \351 \344\356\353\346\355\373 \357\356\353\363\367\350\362\374 \362 \356\346\344\345\361\362\342\356 \350\353\350 \350\347-\347\340 \356 \343\360\340\355\350\367\345\355\355\356\343\356 \367\350\361\353\340 \+ " }}{PARA 0 "" 0 "" {TEXT -1 45 "\367\353\345\355\356\342 \360\377\344 \340 \362\356\353\374\352\356 \357\360\350\341\353\350\347\350\362\345 \353\374\355\356\345 \362\356\346\344\345\361\362\342\356." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(re):" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 81 "\317\356\353\363\367\345\355\355\356\345 \362\356 \346\344\345\361\362\342\356 (\345\343\356 \353\345\342\363\376 \367 \340\361\362\374) \357\360\356\350\353\353\376\361\362\360\350\360\363 \345\354 \343\360\340\364\350\367\345\361\352\350. \304\353\377 \375 \362\356\343\356 \360\340\361-" }}{PARA 0 "" 0 "" {TEXT -1 16 "\361 \354\356\362\360\350\354 \364\363\355\352\366\350\376 " }{TEXT 418 2 " Un" }{TEXT -1 1 "(" }{TEXT 419 1 "x" }{TEXT -1 1 "," }{TEXT 420 1 "t" }{TEXT -1 34 ") \361 \356\343\360\340\355\350\367\345\355\355\373\354 \+ \367\350\361\353\356\354 \361\353\340\343\340\345\354\373\365." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "ren:=subs(u(x,t)=Un(x,t),de) :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "\302 \360\345\347\363\353 \374\362\340\362\345 \357\356\353\363\367\350\354 \357\356\342\345\360 \365\355\356\361\362\374 " }{TEXT 484 3 "lhs" }{TEXT -1 1 "(" }{TEXT 485 3 "ren" }{TEXT -1 32 "), \352\356\362\356\360\363\376 \357\360\345 \344\361\362\340\342\350\354 \343\360\340\364\350\367\345\361\352\350 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "plot3d(lhs(ren), x=0.. 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