Типовые
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Задача 25. Решить первую смешанную задачу для волнового уравнения в прямоугольнике.
25.1utt= u,
ut=0=(xy/64)(2−x)(3−y), ut t=0=0, ux=0= uy =0= ux=2= uy=3=0
25.3utt=9 u,
ut=0=xy(4−x)(5−y), ut t=0=0, ux=0= uy =0= ux=4= uy=5=0
25.5utt=25 u,
ut=0=xy(6−x)(2−y), ut t=0=0, ux=0= uy =0= ux=6= uy=2=0
25.7utt=9 u,
ut=0=xy(3−x)(5−y), ut t=0=0, ux=0= uy =0= ux=3= uy=5=0
25.9utt=25 u,
ut=0=xy(5−x)(2−y), ut t=0=0, ux=0= uy =0= ux=5= uy=2=0
25.11utt=9 u,
ut=0=xy(2−x)(5−y), ut t=0=0, ux=0= uy =0= ux=2= uy=5=0
25.13utt=25 u,
ut=0=xy(4−x)(2−y), ut t=0=0, ux=0= uy =0= ux=4= uy=2=0
25.15utt=4 u,
ut=0=xy(6−x)(4−y), ut t=0=0, ux=0= uy =0= ux=6= uy=4=0
25.2utt=4 u,
ut=0=xy(3−x)(4−y), ut t=0=0,
ux=0= uy =0= ux=3= uy=4=0
25.4utt=16 u,
ut=0=xy(5−x)(6−y), ut t=0=0, ux=0= uy =0= ux=5= uy=6=0
25.6utt=4 u,
ut=0=xy(2−x)(4−y), ut t=0=0, ux=0= uy =0= ux=2= uy=4=0
25.8utt=16 u,
ut=0=xy(4−x)(6−y), ut t=0=0, ux=0= uy =0= ux=4= uy=6=0
25.10 utt= u,
ut=0=xy(6−x)(3−y), ut t=0=0, ux=0= uy =0= ux=6= uy=3=0
25.12 utt=16 u,
ut=0=xy(3−x)(6−y), ut t=0=0, ux=0= uy =0= ux=3= uy=6=0
25.14 utt= u,
ut=0=xy(5−x)(3−y), ut t=0=0, ux=0= uy =0= ux=5= uy=3=0
25.16 utt=16 u,
ut=0=xy(2−x)(6−y), ut t=0=0,
ux=0= uy =0= ux=2= uy=6=0
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25.17utt=25 u,
ut=0=xy(3−x)(2−y), ut t=0=0, ux=0= uy =0= ux=3= uy=2=0
25.19utt=4 u,
ut=0=xy(5−x)(4−y), ut t=0=0, ux=0= uy =0= ux=5= uy=4=0
25.21utt=25 u,
ut=0=xy(2−x)(2−y), ut t=0=0, ux=0= uy =0= ux=2= uy=2=0
25.23utt=4 u,
ut=0=xy(4−x)(4−y), ut t=0=0, ux=0= uy =0= ux=4= uy=4=0
25.25utt=16 u,
ut=0=xy(6−x)(6−y), ut t=0=0, ux=0= uy =0= ux=6= uy=6=0
25.27 utt=121 u, ut=0=xy(3−x)(6−y), ut t=0=0,
ux=0= uy =0= ux=3= uy=6=0
25.29 utt=81 u,
ut=0=xy(5−x)(4−y), ut t=0=0, ux=0= uy =0= ux=5= uy=4=0
25.31utt=49 u,
ut=0=xy(7−x)(2−y), ut t=0=0, ux=0= uy =0= ux=7= uy=2=0
25.18 utt= u,
ut=0=xy(4−x)(3−y), ut t=0=0,
ux=0= uy =0= ux=4= uy=3=0
25.20 utt=9 u,
ut=0=xy(6−x)(5−y), ut t=0=0, ux=0= uy =0= ux=6= uy=5=0
25.22 utt= u,
ut=0=xy(3−x)(3−y), ut t=0=0, ux=0= uy =0= ux=3= uy=3=0
25.24 utt=9 u,
ut=0=xy(5−x)(5−y), ut t=0=0, ux=0= uy =0= ux=5= uy=5=0
25.26 utt=144 u,
ut=0=xy(2−x)(7−y), ut t=0=0, ux=0= uy =0= ux=2= uy=7=0
25.28 utt=100 u,
ut=0=xy(4−x)(5−y), ut t=0=0, ux=0= uy =0= ux=4= uy=5=0
25.30 utt=64 u,
ut=0=xy(6−x)(3−y), ut t=0=0,
ux=0= uy =0= ux=6= uy=3=0
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Задача 26. Решить первую смешанную задачу для волнового уравнения в круге.
26.1utt= u, 0≤ r< 25, 0< t < ∞, u(r,0)=1/8[1−(r/25)2],
ut(r,0)=0, u(25,t)=0
26.2utt=2 u, 0≤ r< 24, 0< t < ∞, u(r,0)=1/8[1−(r/24)2],
ut(r,0)=0, u(24,t)=0
26.3utt=3 u, 0≤ r< 23, 0< t < ∞, u(r,0)=1/8[1−(r/23)2],
ut(r,0)=0, u(23,t)=0
26.4utt=4 u, 0≤ r< 22, 0< t < ∞, u(r,0)=1/8[1−(r/22)2],
ut(r,0)=0, u(22,t)=0
26.5utt=5 u, 0≤ r< 21, 0< t < ∞, u(r,0)=1/8[1−(r/21)2],
ut(r,0)=0, u(21,t)=0
26.7utt=7 u, 0≤ r< 19, 0< t < ∞, u(r,0)=1/8[1−(r/19)2],
ut(r,0)=0, u(19,t)=0
26.9utt=9 u, 0≤ r< 17, 0< t < ∞, u(r,0)=1/8[1−(r/17)2],
ut(r,0)=0, u(17,t)=0
26.11utt=11 u, 0≤ r< 15, 0< t < ∞, u(r,0)=1/8[1−(r/15)2],
ut(r,0)=0, u(15,t)=0
26.13utt=13 u, 0≤ r< 13, 0< t < ∞, u(r,0)=1/8[1−(r/13)2],
ut(r,0)=0, u(13,t)=0
26.15utt=15 u, 0≤ r< 11, 0< t < ∞, u(r,0)=1/8[1−(r/11)2],
ut(r,0)=0, u(11,t)=0
26.6utt=6 u, 0≤ r< 20, 0< t < ∞, u(r,0)=1/8[1−(r/20)2],
ut(r,0)=0, u(20,t)=0
26.8utt=8 u, 0≤ r< 18, 0< t < ∞, u(r,0)=1/8[1−(r/18)2],
ut(r,0)=0, u(18,t)=0
26.10utt=10 u, 0≤ r< 16, 0< t < ∞, u(r,0)=1/8[1−(r/16)2],
ut(r,0)=0, u(16,t)=0
26.12utt=12 u, 0≤ r< 14, 0< t < ∞, u(r,0)=1/8[1−(r/14)2],
ut(r,0)=0, u(14,t)=0
26.14utt=14 u, 0≤ r< 12, 0< t < ∞, u(r,0)=1/8[1−(r/12)2],
ut(r,0)=0, u(12,t)=0
26.16utt=16 u, 0≤ r< 10, 0< t < ∞, u(r,0)=1/8[1−(r/10)2],
ut(r,0)=0, u(10,t)=0
26.17utt=17 u, 0≤ r< 9, 0< t < ∞, u(r,0)=1/8[1−(r/9)2],
ut(r,0)=0, u(9,t)=0
26.19utt=19 u, 0≤ r< 7, 0< t < ∞, u(r,0)=1/8[1−(r/7)2],
ut(r,0)=0, u(7,t)=0
26.21utt=21 u, 0≤ r< 5, 0< t < ∞, u(r,0)=1/8[1−(r/5)2],
ut(r,0)=0, u(5,t)=0
26.23utt=23 u, 0≤ r< 3, 0< t < ∞, u(r,0)=1/8[1−(r/3)2],
ut(r,0)=0, u(3,t)=0
26.25utt=25 u, 0≤ r< 1, 0< t < ∞, u(r,0)=1/8[1−(r)2],
ut(r,0)=0, u(1,t)=0
26.27utt=4 u, 0≤ r< 5, 0< t < ∞, u(r,0)=1/8[1−(r/5)2],
ut(r,0)=0, u(5,t)=0
26.29utt=16 u, 0≤ r< 3, 0< t < ∞, u(r,0)=1/8[1−(r/3)2],
ut(r,0)=0, u(3,t)=0
26.31 utt=36 u, 0≤ r< 1, 0< t < ∞, u(r,0)=1/8[1−(r)2],
ut(r,0)=0, u(1,t)=0
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26.18utt=18 u, 0≤ r< 8, 0< t < ∞, u(r,0)=1/8[1−(r/8)2],
ut(r,0)=0, u(8,t)=0
26.20utt=20 u, 0≤ r< 6, 0< t < ∞, u(r,0)=1/8[1−(r/6)2],
ut(r,0)=0, u(6,t)=0
26.22utt=22 u, 0≤ r< 4, 0< t < ∞, u(r,0)=1/8[1−(r/4)2],
ut(r,0)=0, u(4,t)=0
26.24utt=24 u, 0≤ r< 2, 0< t < ∞, u(r,0)=1/8[1−(r/2)2],
ut(r,0)=0, u(2,t)=0
26.26utt= u, 0≤ r< 6, 0< t < ∞, u(r,0)=1/8[1−(r/6)2],
ut(r,0)=0, u(6,t)=0
26.28utt=9 u, 0≤ r< 4, 0< t < ∞, u(r,0)=1/8[1−(r/4)2],
ut(r,0)=0, u(4,t)=0
26.30utt=25 u, 0≤ r< 2, 0< t < ∞, u(r,0)=1/8[1−(r/2)2],
ut(r,0)=0, u(2,t)=0
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Задача 27. Найти решение первой смешанной задачи для уравнения
теплопроводности на отрезке. |
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27.1 ut=16uxx,0< x <3 ,t>0, |
27.2 ut=uxx,0< x < 2,t>0, |
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/ 3, 0 < x ≤,3 / 2 |
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0 ≤ x ≤ 1, |
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u(x,0)= x |
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u(x,0)= x |
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− x, 3 / 2 < x ≤ 3, |
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− x, 1 < x ≤ 2, |
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3 |
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u(0,t)=u(3,t)=0 |
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u(0,t)=u(2,t)=0 |
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27.3 ut=25uxx,0< x < 5,t>0, |
27.4 ut=16uxx,0< x <4 ,t>0, |
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2 |
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0 ≤ x ≤ 5 / 2, |
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2 |
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0 ≤ x ≤ 2, |
u(x,0)= 2x |
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/ 5, |
u(x,0)= x |
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/ 2, |
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− x, 5 / 2 < x ≤ 5, |
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− x, 2 < x ≤ 4, |
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5 |
4 |
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u(0,t)=u(5,t)=0 |
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u(0,t)=u(4,t)=0 |
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27.5 ut=4uxx,0< x < 5,t>0, |
27.6 ut=uxx,0< x < 3,t>0, |
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2 |
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0 ≤ x ≤ 5 / 2, |
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2 |
/ 3, 0 ≤ x ≤ 3 / 2, |
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u(x,0)= 2x |
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/ 5, |
u(x,0)= 2x |
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− x, 5 / 2 < x ≤ 5, |
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− x, 3 / 2 < x ≤ 3, |
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5 |
3 |
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u(0,t)=u(5,t)=0 |
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u(0,t)=u(3,t)=0 |
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27.7 ut=25uxx,0< x < 8,t>0, |
27.8 ut=9uxx,0< x < 2,t>0, |
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/ 4, 0 ≤ x ≤ 4, |
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2 |
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0 ≤ x ≤ 1, |
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u(x,0)= x |
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u(x,0)= x |
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− x, 4 < x ≤ 8, |
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− x, 1 < x ≤ 2, |
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2 |
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u(0,t)=u(8,t)=0 |
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u(0,t)=u(2,t)=0 |
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27.9 ut=16uxx,0< x <1 ,t>0, |
27.10 ut=4uxx,0< x < 4,t>0, |
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2 |
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≤ x ≤ 1 / 2, |
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2 |
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0 ≤ x ≤ 2, |
u(x,0)= 2x |
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u(x,0)= x |
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/ 2, |
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− x, 2 < x ≤ 4, |
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1− x, 1 / 2 < x ≤ 1, |
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u(0,t)=u(1,t)=0 |
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u(0,t)=u(4,t)=0 |
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27.11 ut=9uxx,0< x < 10,t>0, |
27.12 ut=25uxx,0< x < 9,t>0, |
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/ 5, 0 ≤ x ≤,5 |
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/ 9, 0 ≤ x ≤ 9 / 2, |
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u(x,0)= x |
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u(x,0)= 2x |
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5 < x ≤ 10, |
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− x, |
9 / 2 < x ≤ 9, |
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10 − x, |
9 |
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u(0,t)=u(10,t)=0 |
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u(0,t)=u(9,t)=0 |
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27.13 ut=9uxx,0< x <3, t>0, |
27.14 ut=uxx,0< x < 5,t>0, |
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2 |
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0 ≤ x ≤,3 / 2 |
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2 |
/ 5, 0 ≤ x ≤ 5 / 2, |
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u(x,0)= 2x |
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/ 3, |
u(x,0)= 2x |
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− x, 3 / 2 < x ≤ 3, |
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− x, 5 / 2 < x ≤ 5, |
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5 |
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u(0,t)=u(3,t)=0 |
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u(0,t)=u(5,t)=0 |
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27.15 ut=4uxx,0< x < 7,t>0, |
27.16 ut=25uxx,0< x < 1,t>0, |
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2 |
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0 ≤ x ≤,7 / 2 |
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2 |
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u(x,0)= 2x |
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/ 7, |
u(x,0)= 2x |
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− x, 7 / 2 < x ≤ 7, |
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1 − x, 1 / 2 < x ≤ 1, |
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u(0,t)=u(7,t)=0 |
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u(0,t)=u(1,t)=0 |
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27.17 ut=9uxx,0< x < 4,t>0,
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2 |
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0 ≤ x ≤ 2, |
u(x,0)= x |
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/ 2, |
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− x, |
2 < x ≤ 4, |
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4 |
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u(0,t)=u(4,t)=0 |
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27.19 ut=4uxx,0< x < 2,t>0, |
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≤ x ≤ 1, |
u(x,0)= x |
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0 |
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− x, |
1 < x ≤ 2, |
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2 |
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u(0,t)=u(2,t)=0 |
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27.21 ut=uxx,0< x < 1,t>0, |
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2 |
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u(x,0)= 2x |
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1− x, 1 / 2 < x ≤ 1, |
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u(0,t)=u(1,t)=0 |
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27.23 ut=16uxx,0< x < 6,t>0, |
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0 ≤ x ≤ 3, |
u(x,0)= x |
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/ 3, |
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− x, |
3 < x ≤ 6, |
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6 |
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u(0,t)=u(6,t)=0 |
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27.25 ut=9uxx,0< x < 5,t>0, |
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2 |
/ 5, 0 ≤ x ≤ 5 / 2, |
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u(x,0)= 2x |
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− x, 5 / 2 < x ≤ 5, |
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5 |
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u(0,t)=u(5,t)=0 |
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27.27 ut=uxx,0< x < 12,t>0, |
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0 ≤ x ≤ 6, |
u(x,0)= x |
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/ 6, |
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12 − x, 6 < x ≤ 12, |
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u(0,t)=u(12,t)=0 |
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27.29 ut=4uxx,0< x < 6,t>0, |
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0 ≤ x ≤ 3, |
u(x,0)= x |
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/ 3, |
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− x, |
3 < x ≤ 6, |
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6 |
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u(0,t)=u(6,t)=0 |
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27.31 ut=9uxx,0< x <8 ,t>0, |
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0 ≤ x ≤ 4, |
u(x,0)= x |
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/ 4, |
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− x, 4 < x ≤ 8, |
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8 |
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u(0,t)=u(8,t)=0
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27.18 ut=uxx,0< x < 10,t>0,
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0 ≤ x ≤ 5, |
u(x,0)= x |
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/ 5, |
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5 < x ≤ 10, |
10 − x, |
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u(0,t)=u(10,t)=0 |
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27.20 ut=16uxx,0< x < 8,t>0, |
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0 ≤ x ≤ 4, |
u(x,0)= x |
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/ 4, |
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− x, |
4 < x ≤ 8, |
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8 |
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u(0,t)=u(8,t)=0 |
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27.22 ut=25uxx,0< x < 4,t>0, |
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0 ≤ x ≤ 2, |
u(x,0)= x |
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/ 2, |
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− x, |
2 < x ≤ 4, |
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4 |
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u(0,t)=u(4,t)=0 |
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27.24 ut=4uxx,0< x < 1,t>0, |
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2 |
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u(x,0)= 2x |
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1− x, 1 / 2 < x ≤ 1, |
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u(0,t)=u(1,t)=0 |
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27.26 ut=25uxx,0< x <6 ,t>0, |
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0 ≤ x ≤ 3, |
u(x,0)= x |
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/ 3, |
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− x, |
3 < x ≤ 6, |
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6 |
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u(0,t)=u(6,t)=0 |
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27.28 ut=16uxx,0< x <2 ,t>0, |
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≤ x ≤ 1, |
u(x,0)= x |
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0 |
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− x, |
1 < x ≤ 2, |
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u(0,t)=u(2,t)=0 |
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27.30 ut=36uxx,0< x <3 ,t>0, |
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0 ≤ x ≤ 3 / 2, |
u(x,0)= x |
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/ 3, |
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− x, 3 / 2 < x ≤ 3, |
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3 |
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u(0,t)=u(3,t)=0
37
Задача 28. Найти решение первой смешанной задачи для уравнения теплопроводности в круге.
28.1ut=16 u, 0≤ r < 5 , t>0, u(r,0)=25−r2,
u(5,t)=0
28.3ut= u, 0≤ r < 7 , t>0, u(r,0)=49−r2,
u(7,t)=0
28.5ut=9 u, 0≤ r < 8 , t>0, u(r,0)=64−r2,
u(8,t)=0
28.7ut=16 u, 0≤ r < 1 , t>0, u(r,0)=1−r2,
u(1,t)=0
28.9ut=5 u, 0≤ r < 4, t>0, u(r,0)=16−r2,
u(4,t)=0
28.11ut=10 u, 0≤ r < 2 , t>0, u(r,0)=4−r2,
u(2,t)=0
28.13ut=6 u, 0≤ r < 6 , t>0, u(r,0)=36−r2,
u(6,t)=0
28.15ut=7 u, 0≤ r < 5 , t>0, u(r,0)=25−r2,
u(5,t)=0
28.2ut=25 u, 0≤ r < 3 , t>0, u(r,0)=9−r2,
u(3,t)=0
28.4ut=10 u, 0≤ r < 1 , t>0, u(r,0)=1−r2,
u(1,t)=0
28.6ut=25 u, 0≤ r < 2 , t>0, u(r,0)=4−r2,
u(2,t)=0
28.8ut=3 u, 0≤ r < 3 , t>0, u(r,0)=9−r2,
u(3,t)=0
28.10ut= u, 0≤ r < 5 , t>0, u(r,0)=25−r2,
u(5,t)=0
28.12ut=25 u, 0≤ r < 4 , t>0, u(r,0)=16−r2,
u(4,t)=0
28.14ut=4 u, 0≤ r < 1 , t>0, u(r,0)=1−r2,
u(1,t)=0
28.16ut=10 u, 0≤ r < 7 , t>0, u(r,0)=49−r2,
u(7,t)=0
28.17ut= u, 0≤ r < 1 , t>0, u(r,0)=1−r2,
u(1,t)=0
28.19ut=9 u, 0≤ r < 3 , t>0, u(r,0)=9−r2,
u(3,t)=0
28.21ut=36 u, 0≤ r < 7 , t>0, u(r,0)=49−r2,
u(7,t)=0
28.23ut= u, 0≤ r < 4 , t>0, u(r,0)=16−r2,
u(4,t)=0
28.25ut=2 u, 0≤ r < 3 , t>0, u(r,0)=9−r2,
u(3,t)=0
28.27ut=5 u, 0≤ r < 1 , t>0, u(r,0)=1−r2,
u(1,t)=0
28.29ut=6 u, 0≤ r < 7 , t>0, u(r,0)=49−r2,
u(7,t)=0
28.31ut=7 u, 0≤ r < 4 , t>0, u(r,0)=16−r2,
u(4,t)=0
38
28.18ut= u, 0≤ r < 2 , t>0, u(r,0)=4−r2,
u(2,t)=0
28.20ut=2 u, 0≤ r < 4 , t>0, u(r,0)=16−r2,
u(4,t)=0
28.22ut=4 u, 0≤ r < 2 , t>0, u(r,0)=4−r2,
u(2,t)=0
28.24ut=25 u, 0≤ r < 5 , t>0, u(r,0)=25−r2,
u(5,t)=0
28.26ut=3 u, 0≤ r < 6 , t>0, u(r,0)=36−r2,
u(6,t)=0
28.28ut=9 u, 0≤ r < 2 , t>0, u(r,0)=4−r2,
u(2,t)=0
28.30ut=4 u, 0≤ r < 8 , t>0, u(r,0)=64−r2,
u(8,t)=0
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Задача 29. Используя формулу Пуассона, найти решение задачи Коши для |
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волнового уравнения на плоскости. |
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29.1 utt=a2(uxx+uyy) |
29.2 utt=a2(uxx+uyy) |
ut=0=0, ut t=0=(x+y)2
29.3utt=a2(uxx+uyy)
ut=0=0, ut t=0=(2x+y)2
29.5utt=a2(uxx+uyy)
ut=0=0, ut t=0=(2x−y)2
29.7utt=a2(uxx+uyy)
ut=0=0, ut t=0=(3x+y)2
29.9utt=a2(uxx+uyy)
ut=0=0, ut t=0=(2x+3y)2
29.11utt=a2(uxx+uyy)
ut=0=0, ut t=0=(3x+4y)2
29.13utt=a2(uxx+uyy)
ut=0=0, ut t=0=(5x+6y)2
29.15utt=a2(uxx+uyy)
ut=0=0, ut t=0=(6x+7y)2
29.17utt=a2(uxx+uyy) ut=0=3x2+4y2, ut t=0=0
29.19utt=a2(uxx+uyy) ut=0=4x2+5y2, ut t=0=0
29.21utt=a2(uxx+uyy) ut=0=5x2+6y2, ut t=0=0
29.23utt=a2(uxx+uyy) ut=0=6x2+7y2, ut t=0=0
29.25utt=a2(uxx+uyy) ut=0=x2+y2, ut t=0=0
29.27utt=a2(uxx+uyy) ut=0=2x2+1y2, ut t=0=0
29.29utt=a2(uxx+uyy) ut=0=y2−x2, ut t=0=0
29.31utt=a2(uxx+uyy) ut=0=3x2+y2, ut t=0=0
ut=0=0, ut t=0=(x−y)2
29.4utt=a2(uxx+uyy)
ut=0=0, ut t=0=(x+2y)2
29.6utt=a2(uxx+uyy)
ut=0=0, ut t=0=(x−2y)2
29.8utt=a2(uxx+uyy)
ut=0=0, ut t=0=(x−3y)2
29.10utt=a2(uxx+uyy)
ut=0=0, ut t=0=(2x−3y)2
29.12utt=a2(uxx+uyy)
ut=0=0, ut t=0=(3x−4y)2
29.14utt=a2(uxx+uyy)
ut=0=0, ut t=0=(5x−6y)2
29.16utt=a2(uxx+uyy)
ut=0=0, ut t=0=(6x−7y)2
29.18utt=a2(uxx+uyy)
ut=0= 3x2−4y2, ut t=0=0
29.20utt=a2(uxx+uyy)
ut=0= 4x2−5y2, ut t=0=0
29.22 utt=a2(uxx+uyy)
ut=0= 5x2−6y2, ut t=0=0
29.24 utt=a2(uxx+uyy)
ut=0= 6x2−7y2, ut t=0=0
29.26 utt=a2(uxx+uyy)
ut=0= x2−y2, ut t=0=0
29.28 utt=a2(uxx+uyy)
ut=0= x2+2y2, ut t=0=0
29.30utt=a2(uxx+uyy)
ut=0= 3x2+2y2, ut t=0=0
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Задача 30. Используя формулу Кирхгофа, найти решение задачи Коши для |
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30.1 utt=uxx+uyy+uxz, |
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30.2 |
utt=2(uxx+uyy+uxz), |
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ut=0=0, ut t=0=(x−y+z)2 |
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ut=0=0, ut t=0=(x−2y+z)2 |
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30.3 utt=3(uxx+uyy+uxz), |
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30.4 |
utt=4(uxx+uyy+uxz), |
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ut=0=0, ut t=0=(x+y−z)2 |
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ut=0=0, ut t=0=(x+y−2z)2 |
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30.5 utt=5(uxx+uyy+uxz), |
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30.6 |
utt=6(uxx+uyy+uxz) |
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u |
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t=0 |
=(2x+y+2z)2 |
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t=0 |
t=0 |
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t=0 |
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30.7 utt=7(uxx+uyy+uxz), |
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30.8 |
utt=8(uxx+uyy+uxz), |
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=0, ut |
=(x+y+3z)2 |
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u |
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t=0 |
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t=0 |
t=0 |
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t=0 |
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30.9 utt=9(uxx+uyy+uxz), |
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30.10 |
utt=10(uxx+uyy+uxz) |
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=0, ut |
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u |
=0, ut |
t=0 |
=(3x+2y+4z)2 |
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t=0 |
t=0 |
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t=0 |
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30.11 |
utt=11(uxx+uyy+uxz), |
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30.12 |
utt=12(uxx+uyy+uxz) |
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u |
=0, ut |
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u |
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t=0 |
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t=0 |
t=0 |
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t=0 |
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30.13 |
utt=13(uxx+uyy+uxz), |
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30.14 |
utt=14(uxx+uyy+uxz), |
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u |
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t=0 |
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t=0 |
t=0 |
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t=0 |
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30.15 |
utt=15(uxx+uyy+uxz), |
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30.16 |
utt=16(uxx+uyy+uxz), |
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u |
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u |
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t=0 |
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t=0 |
t=0 |
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t=0 |
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30.17 |
utt=15(uxx+uyy+uxz), |
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30.18 |
utt=14(uxx+uyy+uxz), |
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ut=0=x2−y2+z2, ut t=0=0 |
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ut=0=x2−2y2+z2, ut t=0=0 |
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30.19 |
utt=13(uxx+uyy+uxz), |
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30.20 |
utt=12(uxx+uyy+uxz), |
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u |
=x2+y2−z2, ut |
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u |
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t=0 |
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t=0 |
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t=0 |
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t=0 |
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30.21 |
utt=11(uxx+uyy+uxz), |
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30.22 |
utt=10(uxx+uyy+uxz), |
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u |
=2x2+y2+2z2, ut |
t=0 |
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u |
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t=0 |
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t=0 |
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t=0 |
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30.23 |
utt=9(uxx+uyy+uxz), |
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30.24 |
utt=8(uxx+uyy+uxz), |
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u |
=x2+y2+3z2, ut |
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u |
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t=0 |
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t=0 |
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t=0 |
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t=0 |
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30.25 |
utt=7(uxx+uyy+uxz), |
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30.26 |
utt=6(uxx+uyy+uxz), |
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u |
=3x2+2y2+z2, ut |
t=0 |
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u |
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t=0 |
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t=0 |
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t=0 |
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30.27 |
utt=5(uxx+uyy+uxz), |
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30.28 |
utt=4(uxx+uyy+uxz), |
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u |
=2x2+y2+3z2, ut |
t=0 |
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u |
=2x2+3y2+z2, ut |
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t=0 |
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t=0 |
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t=0 |
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30.29 |
utt=3(uxx+uyy+uxz), |
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30.30 |
utt=2(uxx+uyy+uxz), |
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u |
=3x2+4y2+5z2, ut =0 |
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u |
=4x2+4y2+3z2, ut |
t=0 |
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t=0 |
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t=0 |
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t=0 |
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30.31utt=uxx+uyy+uxz, ut=0=5x2+3y2+4z2, ut t=0=0