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\par }{\cs20\b\f2\insrsid1920997 f1:=x->x*(L-x); F1:=x->0; }{\insrsid1920997 
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\'e8\'e4\'e5 \'f0\'ff\'e4\'e0. 
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\'ec\'e5\'f2\'ee\'e4\'e8\'ea\'ee\'e9
\par \'e5\'e3\'ee \'ea\'ee\'ec\'ef\'fc\'fe\'f2\'e5\'f0\'ed\'ee\'e3\'ee \'e8\'e7\'eb\'ee\'e6\'e5\'ed\'e8\'ff \'e8 \'ef\'ee\'e7\'e2\'ee\'eb\'ff\'e5\'f2 \'e2\'e5\'f1\'f2\'e8 \'e4\'e5\'f2\'e0\'eb\'fc\'ed\'fb\'e9 \'e0\'ed\'e0\'eb\'e8\'e7 \'ea\'e0\'e6\'e4\'ee\'e3
\'ee \'ef\'f0\'ee\'ec\'e5\'e6\'f3-
\par \'f2\'ee\'f7\'ed\'ee\'e3\'ee \'f0\'e5\'e7\'f3\'eb\'fc\'f2\'e0\'f2\'e0.
\par \'c7\'e0\'ef\'e8\'f8\'e5\'ec  \'e4\'e8\'f4\'f4\'e5\'f0\'e5\'ed\'f6\'e8\'e0\'eb\'fc\'ed\'ee\'e5 \'f3\'f0\'e0\'e2\'ed\'e5\'ed\'e8\'e5 \'f1 \'f7\'e0\'f1\'f2\'ed\'fb\'ec\'e8 \'ef\'f0\'ee\'e8\'e7\'e2\'ee\'e4\'ed\'fb\'ec\'e8, \'f0\'e5\'f8\'e5\'ed\'e8\'e5 \'ea
\'ee\'f2\'ee\'f0\'ee\'e3\'ee
\par \'ea\'e0\'ea \'e1\'fb\'eb\'ee \'f1\'ea\'e0\'e7\'e0\'ed\'ee \'e2\'fb\'f8\'e5 \'f2\'f0\'e5\'e1\'f3\'e5\'f2\'f1\'ff \'ed\'e0\'e9\'f2\'e8, \'e2 \'f3\'e4\'ee\'e1\'ed\'ee\'ec \'e4\'eb\'ff \'e4\'e0\'eb\'fc\'ed\'e5\'e9\'f8\'e8\'f5 \'e2\'fb\'f7\'e8\'f1\'eb\'e5\'ed
\'e8\'e9 \'e2\'e8\'e4\'e5:
\par }{\cs20\b\f2\insrsid1920997 de:=a^2*diff(w(x,t),x$2)-diff(w(x,t),t$2)=0;}{\insrsid1920997 
\par }\pard\plain \s137\qc \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn29\insrsid15206884 {\pict{\*\picprop\shplid1028{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
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\par \'d0\'e5\'f8\'c3\'e8\'ef\'d3\'f0\'c2_}{\insrsid1920997 MapleMWS}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 .}{\insrsid1920997 mws}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 " ) \'ef\'ee\'eb\'f3\'f7\'e8\'eb\'e8 
\'ed\'f3\'eb\'e5\'e2\'fb\'e5 \'e3\'f0\'e0\'ed\'e8\'f7\'ed\'fb\'e5 \'f3\'f1\'eb\'ee\'e2\'e8\'ff: 
\par }{\cs59\i\insrsid1920997 W}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 (0,}{\insrsid1920997 t}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 )=}{\cs81\i\insrsid1920997 w}{
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\par \'e0\'eb\'e3\'ee\'f0\'e8\'f2\'ec\'e0.
\par \'ce\'e1\'f0\'e0\'f2\'e8\'ec \'e2\'ed\'e8\'ec\'e0\'ed\'e8\'e5 \'ed\'e0 \'f1\'e5\'ec\'e0\'ed\'f2\'e8\'ea\'f3 \'ee\'ef\'f6\'e8\'e8 }{\cs78\i\insrsid1920997 assume}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 , \'f3\'ea\'e0\'e7\'fb\'e2\'e0
\'fe\'f9\'e5\'e9 \'ed\'e0 \'f1\'e2\'ee\'e9\'f1\'f2\'e2\'e0 \'ef\'e0\'f0\'e0\'ec\'e5\'f2\'f0\'ee\'e2, 
\par \'f3\'f7\'e0\'f1\'f2\'e2\'f3\'fe\'f9\'e8\'f5 \'e2 \'e2\'fb\'f7\'e8\'f1\'eb\'e5\'ed\'e8\'ff\'f5. \'c1\'f3\'e4\'e5\'ec \'e8\'f1\'ef\'ee\'eb\'fc\'e7\'ee\'e2\'e0\'f2\'fc \'fd\'f2\'f3 \'ee\'ef\'f6\'e8\'fe \'ef\'f0\'e8 \'f3\'ef\'f0\'ee\'f9\'e5\'ed\'e8\'e8 \'e2
\'fb\'f0\'e0\'e6\'e5\'ed\'e8\'e9.
\par \'d3\'ea\'e0\'e6\'e5\'ec \'ed\'e0 \'f1\'e2\'ee\'e9\'f1\'f2\'e2\'ee \'ef\'e0\'f0\'e0\'ec\'e5\'f2\'f0\'e0 }{\cs69\i\insrsid1920997 n}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997  \'e8 \'e2\'e2\'e5\'e4\'e5\'ec \'ee\'e1\'ee\'e7\'ed\'e0\'f7
\'e5\'ed\'e8\'ff:
\par }{\cs20\b\f2\insrsid1920997 assume(n,integer): omegan:=Pi*n*a/L: N:=infinity:}{\insrsid1920997 
\par }{\cs70\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 \'c7\'e0\'ef\'e8\'f8\'e5\'ec  \'ea\'ee\'ec\'ef\'ee\'ed\'e5\'ed\'f2\'f3 }{\cs83\b\i\insrsid1920997 W}{\cs86\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 (}{
\cs84\b\i\insrsid1920997 x}{\cs87\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 ,}{\cs85\b\i\insrsid1920997 t}{\cs88\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 ) \'f0\'e5\'f8\'e5\'ed\'e8\'ff }{
\cs71\b\i\insrsid1920997 u}{\cs110\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 (}{\cs67\b\i\insrsid1920997 x}{\cs72\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 ,}{\cs68\b\i\insrsid1920997 t}{
\cs73\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 )}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 . 
\par \'cd\'e0\'f7\'ed\'e5\'ec \'f1 \'e2\'fb\'f7\'e8\'f1\'eb\'e5\'ed\'e8\'ff \'ea\'ee\'fd\'f4\'f4\'e8\'f6\'e8\'e5\'ed\'f2\'ee\'e2 \'f0\'ff\'e4\'e0 \'d4\'f3\'f0\'fc\'e5:
\par - \'e7\'e0\'ef\'e8\'f8\'e5\'ec \'ea\'ee\'fd\'f4\'f4\'e8\'f6\'e8\'e5\'ed\'f2\'fb \'f0\'ff\'e4\'e0 \'d4\'f3\'f0\'fc\'e5 \'e4\'eb\'ff \'f4\'f3\'ed\'ea\'f6\'e8\'e9 \'ed\'e0\'f7\'e0\'eb\'fc\'ed\'fb\'f5 \'f3\'f1\'eb\'ee\'e2\'e8\'e9:
\par }{\dn28\insrsid15206884 {\pict{\*\picprop\shplid1029{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw7357\pich2408\picwgoal4171\pichgoal1365\wmetafile8\bliptag-1845672535\blipupi96{\*\blipuid 91fd45a94f4a165d36d206d144626f3b}
0100090000034a02000007001c00000000000400000003010800050000000b0200000000050000000c026809bd1c050000002e01180000000500000002010100
0000050000000902000000001c000000fb025cfe0000000000009001000000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577
170a6651040000002d01000007000000210501003b00af07d3170800000021050400203a3d20af0762011c000000fb025cfe0000000000009001010000000400
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0000000000009001000000020700001253796d626f6c00002a0a0a5ca4880a00e8b1f377f1b1f3772040f577170a6651040000002d0102000800000021050300
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0500000013023a07b91708000000fa0200000000000000000000040000002d01040004000000f0010300040000002d01000007000000210501003200d2032107
040000002d01010007000000210501006400d203ec15040000002d0102000700000021050100f300590260080700000021050100f5001f066008070000002105
0100f4002d0360080700000021050100f400010460080700000021050100f400d50460080700000021050100f4004b0560081c000000fb02e8fe000000000000
9001000000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577170a6651040000002d01030007000000210501003000be061d09
1c000000fb02e8fe0000000000009001010000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577170a6651040000002d010500
07000000210501004c00d4008c09040000002d01000007000000210501002800d2038d0b07000000210501002900d203480d07000000210502006631d2032b0a
040000002d01010007000000210501007800d203500c040000002d0102000700000021050100e60028031e100700000021050100e80045051e10070000002105
0100e700fc031e100700000021050100e70071041e100700000021050100f6002803e3140700000021050100f8004505e3140700000021050100f700fc03e314
0700000021050100f7007104e314040000002d010000080000002105030073696e20d203400e08000000fa0200000a00000000000000040000002d0106000500
000014025d03f2100500000013025d03ae14040000002d01040004000000f0010600040000002d01020007000000210501007000be022711040000002d010100
07000000210501006e00be02771207000000210501007800be02b61307000000210501004c00db045d1207000000210501007800d203c1160700000021050100
4c00b808df0e040000002d01000007000000210501002800af07e61907000000210501002900af07b31b07000000210501004100af07b918040000002d01010007000000210501006e00af07a91a030000000000}}{\insrsid1920997 
\par }\pard\plain \s137\qc \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn29\insrsid15206884 {\pict{\*\picprop\shplid1030{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw3328\pich1177\picwgoal1887\pichgoal667\wmetafile8\bliptag-1063293089\blipupi-108{\*\blipuid c09f6f5f62c61dc8b169bc7037c5b8e3}
0100090000036901000006001c00000000000400000003010800050000000b0200000000050000000c029804010d050000002e01180000000500000002010100
00000500000009020000ff001c000000fb025cfe0000000000009001000000020700001253796d626f6c00007c0a0aa6fc880a00e8b1f377f1b1f3772040f577
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13022402850c08000000fa0200000000000000000000040000002d01020004000000f00101001c000000fb025cfe000000000000900100000000040000125469
6d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577e7096630040000002d010100070000002105010034008501ef01070000002105010028008501
2e03070000002105010029008501c20b040000002d01000007000000210501002d008501f1030800000021050300202b20008501ac05040000002d0101000700
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000000009001010000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577e7096630040000002d01030007000000210502006e7e
d400600a040000002d01000007000000210501007000e803fb041c000000fb02e8fe0000000000009001000000000400001254696d6573204e657720526f6d61
6e00e8b1f377f1b1f3772040f577e7096630040000002d010400070000002105010033003703f2051c000000fb025cfe00000000000090010100000004000012
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\par }\pard\plain \ql \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn28\insrsid15206884 {\pict{\*\picprop\shplid1031{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw7445\pich2408\picwgoal4221\pichgoal1365\wmetafile8\bliptag1375582565\blipupi118{\*\blipuid 51fdb965645838f63c60f8c75d2d3b5e}
0100090000036002000007001c00000000000400000003010800050000000b0200000000050000000c026809161d050000002e01180000000500000002010100
0000050000000902000000001c000000fb025cfe0000000000009001000000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577
170a6654040000002d01000007000000210501003b00af073e180800000021050400203a3d20af0774011c000000fb025cfe0000000000009001010000000400
001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577170a6654040000002d01010007000000210501004200af076a001c000000fb025cfe
0000000000009001000000020700001253796d626f6c00002a0a0a5ea4880a00e8b1f377f1b1f3772040f577170a6654040000002d0102000800000021050300
20ae2020af078004040000002d01010007000000210501006e00af07ab0308000000fa0200000a00000000000000040000002d0103000500000014023a07fe06
0500000013023a07241808000000fa0200000000000000000000040000002d01040004000000f0010300040000002d01000007000000210501003200d2033307
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0100f4002d0372080700000021050100f400010472080700000021050100f400d50472080700000021050100f4004b0572081c000000fb02e8fe000000000000
9001000000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577170a6654040000002d01030007000000210501003000be062f09
1c000000fb02e8fe0000000000009001010000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577170a6654040000002d010500
07000000210501004c00d4009e09040000002d01000007000000210501002800d203f80b07000000210501002900d203b30d07000000210502004631d2033d0a
040000002d01010007000000210501007800d203bb0c040000002d0102000700000021050100e600280389100700000021050100e80045058910070000002105
0100e700fc0389100700000021050100e700710489100700000021050100f60028034e150700000021050100f80045054e150700000021050100f700fc034e15
0700000021050100f70071044e15040000002d010000080000002105030073696e20d203ab0e08000000fa0200000a00000000000000040000002d0106000500
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07000000210501006e00be02e21207000000210501007800be02211407000000210501004c00db04c81207000000210501007800d2032c17040000002d010200
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01002800af073f1a07000000210501002900af070c1c07000000210501004200af072419040000002d01010007000000210501006e00af07021b030000000000}}{\insrsid1920997 
\par }\pard\plain \s137\qc \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn7\insrsid15206884 {\pict{\*\picprop\shplid1032{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw443\pich496\picwgoal251\pichgoal281\wmetafile8\bliptag494279109\blipupi2540{\*\blipuid 1d7619c57746d3cbb4fafd1744fc69bc}0100090000035000000001001c00000000000400000003010800050000000b0200000000050000000c02ef01bb01050000002e01180000000500000002010100
00000500000009020000ff001c000000fb025cfe0000000000009001000000000400001254696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5779c0966a5040000002d010000070000002105010030003f016a00030000000000}}{\insrsid1920997 
\par }\pard\plain \ql \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 \'d2\'e5\'ef\'e5\'f0\'fc \'e7\'e0\'ef\'e8\'f8\'e5\'ec \'e2\'fb\'f0\'e0
\'e6\'e5\'ed\'e8\'e5 \'ea\'ee\'ec\'ef\'ee\'ed\'e5\'ed\'f2\'fb }{\cs89\i\insrsid1920997 W}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 (}{\cs90\i\insrsid1920997 x}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 ,}{
\cs91\i\insrsid1920997 t}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 ): 
\par }{\dn101\insrsid15206884 {\pict{\*\picprop\shplid1033{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw14101\pich1842\picwgoal7994\pichgoal1044\wmetafile8\bliptag502151611\blipupi294{\*\blipuid 1dee39bbed0217387a680c90d0f00fd3}
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\insrsid1920997 
\par }\pard\plain \s137\qc \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn32\insrsid15206884 {\pict{\*\picprop\shplid1034{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw8729\pich1256\picwgoal4949\pichgoal712\wmetafile8\bliptag-490473019\blipupi150{\*\blipuid e2c3f9c55ee5d54fd27528c6178a99c8}
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\par }\pard\plain \ql \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\cs75\b\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 \'c8\'f2\'e0\'ea, \'e8\'ec\'e5\'e5\'ec \'f0\'e5\'f8\'e5\'ed\'e8
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\'fc\'ed\'ee\'ec \'e2\'e8\'e4\'e5}{\lang1049\langfe1049\langnp1049\insrsid1920997\charrsid1920997 :
\par }{\cs20\b\f2\insrsid1920997 W(x,t):=simplify(W(x,t));}{\insrsid1920997 
\par }\pard\plain \s138\ql \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn69\insrsid15206884 {\pict{\*\picprop\shplid1035{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
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