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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "`u(x,0):=A*cos(Pi*x/L)` :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "\341) \343\360\340\355\350 \367\355\373\345:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "u(0,t) :=0; u(L,t):=0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"uG6$\"\"!%\"t GF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"uG6$%\"LG%\"tG\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "`u(0,t):=2; u(L,t):=0;`:" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "\317\345\360\345\357\350\370\345 \354 (\350\353\350 \357\356\344\361\362\340\342\350\354) \352\360\340 \345\342\373\345 \363\361\353\356\342\350\377 \342 d2tU(x,p)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eval(d2tU(x,p));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"pG\"\"#\"\"\"-%(laplaceG6%-%\"uG6$% \"xG%\"tGF0F&F(F(*(F&F(%\"AGF(-%$sinG6#*(%#PiGF(F/F(%\"LG!\"\"F(F9" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "\302\345\360\355\345\354\361\377 \+ \352 \344\350\364\364\345\360\345\355\366\350\340\353\374\355\356\354 \363 \363\360\340\342\355\345\355\350\376 du \350 \347\340\357\350\370 \345\354 \345\343\356 \342 \356\357\345\360\340\362\356\360\355\356 \354 \342\350\344\345:" }}{PARA 0 "" 0 "" {TEXT -1 28 " d2U(x,p)-d2t U(x,p)/a^2=0." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "duo:=d2U(x ,p)-eval(d2tU(x,p))/a^2=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$duoG/ ,&-%%diffG6$-%(laplaceG6%-%\"uG6$%\"xG%\"tGF1%\"pG-%\"$G6$F0\"\"#\"\" \"*&,&*&)F2F6F7F*F7F7*(F2F7%\"AGF7-%$sinG6#*(%#PiGF7F0F7%\"LG!\"\"F7FD F7%\"aG!\"#FD\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "\322\340 \352\350\354 \356\341\360\340\347\356\354, \357\356\353\363\367\350 \353\350 \316\304\323 \356\362\355\356\361\350\362\345\353\374\355\356 \364\363\355\352\366\350\350 Up, \355\356 \363\346\345 \356\362 " } {TEXT 260 1 "\365" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "du0:=subs(laplace(u(x,t),t,p)=Up(x),duo);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$du0G/,&-%%diffG6$-%#UpG6#%\"xG-%\"$G6$F- \"\"#\"\"\"*&,&*&)%\"pGF1F2F*F2F2*(F7F2%\"AGF2-%$sinG6#*(%#PiGF2F-F2% \"LG!\"\"F2F@F2%\"aG!\"#F@\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "\315\340\351\344\345\354 \360\345\370\345\355\350\345 \357\356\353 \363\367\345\355\355\356\343\356 \362\340\352\350\354 \356\341\360\340 \347\356\354 \363\360\340\342\355\345\355\350\377 du0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve(du0,Up(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#UpG6#%\"xG,(*&-%$expG6#*(%\"pG\"\"\"%\"aG!\"\" F'F/F/%$_C2GF/F/*&-F+6#,$F-F1F/%$_C1GF/F/*,%\"AGF/%\"LG\"\"#F.F/-%$sin G6#*(%#PiGF/F'F/F:F1F/,&*&)F.F;F/)F:F;F/F/*&)F@F;F/)F0F;F/F/F1F/" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "*) \310\353\350, \363\367\350\362 \373\342\340\377 \343\360\340\355\350\367\355\373\345 \363\361\353 \356\342\350\377 \356\360\350\343\350\355\340\353\340, \352\356\362 \356\360\373\354 \342 \361\350\353\363 (1) \361\356\356\362\342\345 \362\361\362\342\363\376\362 " }}{PARA 0 "" 0 "" {TEXT -1 80 "\350\347 \356\341\360\340\346\345\355\350\377 U(0,t) = U(L,t) = 0, \347\340 \357\350\370\345\354 \343\360\340\355\350\367\355\373\345 \363\361\353 \356\342\350\377 \344\353\377 Up(x) \357\356\344 \356\344\355\350\354 \+ " }}{PARA 0 "" 0 "" {TEXT -1 7 "\350\354\345\355\345\354 " }{TEXT 261 3 "xUg" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "xUg:=Up(0)=0, Up( L)=0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xUgG6$/-%#UpG6#\"\"!F*/- F(6#%\"LGF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "`xUg:=Up(0)= 2, Up(L)=0;`: " }{TEXT -1 5 "- \355\345\362" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 61 "\350 \361\355\356\342\340 \355\340\351\344\270\354 \360 \345\370\345\355\350\345 du0, \355\356 \363\346\345 \361 \363\367\270 \362\356\354 \343\360\340\355\350\367\355\373\365 \363\361\353\356\342 \350\351" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "UP:=dsolve(\{du 0,xUg\},Up(x)); `Uup(x):=simplify(Up(x));`:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#UPG/-%#UpG6#%\"xG*,%\"AG\"\"\"%\"LG\"\"#%\"pGF,-%$si nG6#*(%#PiGF,F)F,F-!\"\"F,,&*&)F/F.F,)F-F.F,F,*&)F4F.F,)%\"aGF.F,F,F5 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "\315\340\351\344\345\355\355 \356\345 \360\345\370\345\355\350\345 Up(x) \357\360\345\344\361\362 \340\342\353\377\345\362 \361\356\341\356\376 \350\347\356\341\360\340 \346\345\355\350\345 \362\356\343\356 \356\360\350\343\350\355\340\353 \340, \352\356\362\356\360\373\351 " }}{PARA 0 "" 0 "" {TEXT -1 81 " \361\353\345\344\363\345\362 \355\340\351\362\350, \342 \352\356\355 \345\367\355\356\354 \361\367\345\362\345. \304\353\377 \355\340\365 \356\346\344\345\355\350\377 \356\360\350\343\350\355\340\353\340 \342 \356\361\357\356\353\374\347\363\345\354\361\377 \356\341\360\340\362 \355\373\354 " }}{PARA 0 "" 0 "" {TEXT -1 24 "\357\360\345\356\341\360 \340\347\356\342\340\355\350\345\354 \313\340\357\353\340\361\340:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "resh:=(x,t)->invlaplace(rhs (UP),p,t); resh(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%reshGf*6$% \"xG%\"tG6\"6$%)operatorG%&arrowGF)-%+invlaplaceG6%-%$rhsG6#%#UPG%\"pG 9%F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"AG\"\"\"-%$sinG6#*(%# PiGF%%\"xGF%%\"LG!\"\"F%-%%coshG6#**F*F%,$*&)%\"aG\"\"#F%)F,F6F%F-#F%F 6F,!\"#%\"tGF%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 10 "\317\360\350 \354\345\367\340\355\350\345" }{TEXT -1 81 ". \307\344\345\361\374 cos h(i*z*t) = cos(z*t), \343\344\345 i = (-1)^(1/2), z = Pi*a/L. \327\362 \356 \357\356\344\362\342\345\360\346\344\340\345\362 " }}{PARA 0 "" 0 "" {TEXT -1 15 "\342\373\360\340\346\345\355\350\345 \355\350\346 \345." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "invlaplace(p/(p^2+(P i*a/L)^2),p,t);laplace(cos(b*t),t,p);" "6#C$-%+invlaplaceG6%*&%\"pG\" \"\",&*$F(\"\"#F)*$*(%#PiGF)%\"aGF)%\"LG!\"\"F,F)F2F(%\"tG-%(laplaceG6 %-%$cosG6#*&%\"bGF)F3F)F3F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%cosh G6#**%#PiG\"\"\",$*&)%\"aG\"\"#F()%\"LGF-F(!\"\"#F(F-F/!\"#%\"tGF(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"pG\"\"\",&*$)F$\"\"#F%F%*$)%\"bGF )F%F%!\"\"" 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