ДЗ условия (1175500), страница 2
Текст из файла (страница 2)
D + 2 = 0, 0 6 < 5,5,|=5,5 = 14 sin3 3.7.13. D + 2 = 0, 0 6 < 6,|=6 = 13 sin3 3.7.14. D + 2 = 0, 0 6 < 6,5,|=6,5 = 12 sin3 3.7.15. D + 2 = 0, 0 6 < 7,|=7 = 11 sin3 3.7.16. D + 2 = 0, 0 6 < 7,5,|=7,5 = 10 sin3 3.7.17. D + 2 = 0, 0 6 < 8,|=8 = 9 sin3 3.7.19. D + 2 = 0, 0 6 < 9,|=9 = 7 sin3 3.7.20.
D + 2 = 0, 0 6 < 9,5,|=9,5 = 6 sin3 3.7.21. D + 2 = 0, 0 6 < 10,|=10 = 5 sin3 3.7.22. D + 2 = 0, 0 6 < 10,5,|=10,5 = 4 sin3 3.7.23. D + 2 = 0, 0 6 < 11,|=11 = 3 sin3 3.7.24. D + 2 = 0, 0 6 < 11,5,|=11,5 = 2 sin3 3.7.25. D + 2 = 0, 0 6 < 12,|=12 = sin3 3.7.26. D + 2 = 0, 0 6 < 12,5,|=12,5 = 6 sin3 3.7.27. D + 2 = 0, 0 6 < 13,|=13 = 5 sin3 3.7.28.
D + 2 = 0, 0 6 < 13,5,|=13,5 = 4 sin3 3.7.29. D + 2 = 0, 0 6 < 14,|=14 = 3 sin3 3.7.30. D + 2 = 0, 0 6 < 14,5,|=14,5 = 2 sin3 3.7.31. D + 2 = 0, 0 6 < 16,|=16 = sin3 3.7.18. D + 2 = 0, 0 6 < 8,5,|=8,5 = 8 sin3 3.Задача 8. Найти функцию, удовлетворяющую внутри шара уравнению Гельмгольца и принимающую на границе шара заданное значение.p8.1.
D + = 0, 0 6 < ,2 ⃒⃒= cos j.⃒ = 2p8.2. D + = 0, 0 6 < p, ⃒⃒= cos j.⃒ =p3p8.3. D + = 0, 0 6 <,2 ⃒⃒= cos j.⃒ = 3p23p8.15. D + 16 = 0, 0 6 <,8 ⃒⃒= cos j.⃒ = 3p88.4. D + = 0, 0 6 < 2p, ⃒⃒= cos j.⃒ =2pp8.16. D + 16 = 0, 0 6 < ,2 ⃒⃒= cos j.⃒ = 2pp8.5. D + 4 = 0, 0 6 < ,4 ⃒⃒= cos j.⃒ = 4pp8.17. D + 25 = 0, 0 6 < ,10 ⃒⃒= cos j.⃒ = 10pp8.6. D + 4 = 0, 0 6 < ,2⃒ ⃒= cos j.⃒ = 2pp8.18.
D + 25 = 0, 0 6 < ,5⃒ ⃒= cos j.⃒ = 5p3p8.7. D + 4 = 0, 0 6 <,2 ⃒⃒= cos j.⃒ = 3p23p8.19. D + 25 = 0, 0 6 <,10 ⃒⃒⃒ 3p = cos j. = 108.8. D + 4 = 0, 0 6 < p, ⃒⃒= cos j.⃒ =p2p8.20. D + 15 = 0, 0 6 <,5 ⃒⃒= cos j.⃒ = 2p5p8.9. D + 9 = 0, 0 6 < ,6 ⃒⃒= cos j.⃒ = 6pp8.21. D + 36 = 0, 0 6 < ,12 ⃒⃒= cos j.⃒ = 12pp8.10. D + 9 = 0, 0 6 < ,3 ⃒⃒= cos j.⃒ = 3pp8.22. D + 36 = 0, 0 6 < ,6⃒ ⃒= cos j.⃒ = 6pp8.11. D + 9 = 0, 0 6 < ,2⃒ ⃒= cos j.⃒ = 2pp8.23. D + 36 = 0, 0 6 < ,4 ⃒⃒= cos j.⃒ = 4p2p8.12. D + 9 = 0, 0 6 <,3 ⃒⃒= cos j.⃒ = 2p3p8.24. D + 36 = 0, 0 6 < ,2 ⃒⃒= cos j.⃒ = 2pp8.13. D + 16 = 0, 0 6 < ,8⃒ ⃒= cos j.⃒ = 8pp8.25. D + 49 = 0, 0 6 < ,7⃒ ⃒= cos j.⃒ = 7pp8.14.
D + 16 = 0, 0 6 < ,4 ⃒⃒= cos j.⃒ = 4p2p8.26. D + 49 = 0, 0 6 <,7 ⃒⃒= cos j.⃒ = 2p73p8.27. D + 4 = 0, 0 6 <,4 ⃒⃒= cos j.⃒ = 3p48.29. D + 9 = 0, 0 6 < p, ⃒⃒= cos j.⃒ =p8.28. D + = 0, 0 6 < 3p, ⃒⃒= cos j.⃒ =3p8.30. D + 16 = 0, 0 6 < p, ⃒⃒= cos j.⃒ =p8.31. D + 25 = 0, 0 6 < p, ⃒⃒= cos j.⃒ =pЗадача 9. Решить первую смешанную задачу для волнового уравнения на отрезке.9.1.
= , 0 < < 1, 0 < < ∞,9.9. = , 0 < < 2, 0 < < ∞,(, 0) = ( − 1) , (, 0) = 0,(, 0) = ( − 2) , (, 0) = 0,(0, ) = 0, (1) = 0.(0, ) = 0, (2) = 0.39.2. = , 0(︁< <)︁ 2 , 0 < < ∞,3, (, 0) = 0,(, 0) = −2(︁ )︁3(0, ) = 0, = 0.9.10. = 16 , 0 < < 3, 0 < < ∞,9.3.
= 9 , 0 < < 3, 0 < < ∞,9.11. = 16 , 0 < < 2, 0 < < ∞,2(, 0) = ( − 3) , (, 0) = 0,(0, ) = 0, (3) = 0.(, 0) = ( − 3) , (, 0) = 0,(, 0) = ( − 2) , (, 0) = 0,(0, ) = 0, (3) = 0.(0, ) = 0, (2) = 0.9.4. = 4 , 0 < < 2, 0 < < ∞,9.12. = 9 , 0 < < 1, 0 < < ∞,(, 0) = ( − 2) , (, 0) = 0,(, 0) = ( − 1) , (, 0) = 0,(0, ) = 0, (2) = 0.(0, ) = 0, (1) = 0.11119.5.
= 4 , (︁0 < )︁< 2 , 0 < < ∞,1(, 0) = −, (, 0) = 0,2(︁ )︁1(0, ) = 0, = 0.9.13. = 9 , (︁0 < )︁< 2 , 0 < < ∞,1, (, 0) = 0,(, 0) = −2(︁ )︁1(0, ) = 0, = 0.9.6. = 4 , 0 < < 1, 0 < < ∞,9.14. = , 0 < < 3, 0 < < ∞,22(, 0) = ( − 1) , (, 0) = 0,(, 0) = ( − 3) , (, 0) = 0,(0, ) = 0, (1) = 0.(0, ) = 0, (3) = 0.429.7. = 9 , (︁0 < )︁< 3 , 0 < < ∞,2(, 0) = −, (, 0) = 0,3(︁ )︁2= 0.(0, ) = 0, 9.15. = 16 , 0 < < 1, 0 < < ∞,(, 0) = ( − 1) , (, 0) = 0,(0, ) = 0, (1) = 0.31, 0 < < ∞,9.8. = 4 , (︁0 < <)︁ 21(, 0) = −, (, 0) = 0,2(︁ )︁1(0, ) = 0, = 0.23, 0 < < ∞,9.16. = 9 , (︁0 < <)︁ 23(, 0) = −, (, 0) = 0,2(︁ )︁3(0, ) = 0, = 0.29.17.
= 4 , 0 < < 3, 0 < < ∞,(, 0) = ( − 3) , (, 0) = 0,(0, ) = 0, (3) = 0.1, 0 < < ∞,9.25. = 9 , (︁0 < <)︁ 21(, 0) = −, (, 0) = 0,2(︁ )︁1(0, ) = 0, = 0.2149.18. = , 0 < < 2, 0 < < ∞,9.26. = 9 , 0 < < 2, 0 < < ∞,(, 0) = ( − 2) , (, 0) = 0,(, 0) = ( − 2) , (, 0) = 0,(0, ) = 0, (2) = 0.(0, ) = 0, (2) = 0.149.19. = , 0 < < 1, 0 < < ∞,149.27. = , 0 < < 3, 0 < < ∞,(, 0) = ( − 1) , (, 0) = 0,(, 0) = ( − 3) , (, 0) = 0,(0, ) = 0, (1) = 0.(0, ) = 0, (3) = 0.19.20.
= , 0(︁< <)︁ 2 , 0 < < ∞,1(, 0) = −, (, 0) = 0,2(︁ )︁1= 0.(0, ) = 0, 2499.21. = , 0 < < 2, 0 < < ∞,(, 0) = ( − 2) , (, 0) = 0,(0, ) = 0, (2) = 0.9499.28. = , 0 < < 1, 0 < < ∞,(, 0) = ( − 1) , (, 0) = 0,(0, ) = 0, (1) = 0.319.29. = 4 , (︁0 < )︁< 2 , 0 < < ∞,3(, 0) = −, (, 0) = 0,2(︁ )︁3= 0.(0, ) = 0, 239.22.
= 4 , (︁0 < )︁< 2 , 0 < < ∞,3(, 0) = −, (, 0) = 0,2(︁ )︁3= 0.(0, ) = 0, 2199.23. = , 0 < < 1, 0 < < ∞,199.30. = , 0 < < 2, 0 < < ∞,(, 0) = ( − 2) , (, 0) = 0,(0, ) = 0, (2) = 0.949.31. = , 0 < < 1, 0 < < ∞,(, 0) = ( − 1) , (, 0) = 0,(, 0) = ( − 1) , (, 0) = 0,(0, ) = 0, (1) = 0.(0, ) = 0, (1) = 0.949.24. = , 0 < < 3, 0 < < ∞,(, 0) = ( − 3) , (, 0) = 0,(0, ) = 0, (3) = 0.Задача 10. Решить первую смешанную краевой задачу для волнового уравнения в прямоугольнике.10.1. = D,|=0 =(2 − )(3 − ),6410.4. = 16D, |=0 = 0,|=0 = |=0 = |=2 = |=3 = 0.10.2. = 4D,|=0 = (5 − )(6 − ), |=0 = 0,|=0 = |=0 = |=5 = |=6 = 0.10.5.
= 25D,|=0 = (3 − )(4 − ), |=0 = 0,|=0 = (6 − )(2 − ), |=0 = 0,|=0 = |=0 = |=3 = |=4 = 0.|=0 = |=0 = |=6 = |=2 = 0.10.3. = 9D,10.6. = 4D,|=0 = (4 − )(5 − ), |=0 = 0,|=0 = (2 − )(4 − ), |=0 = 0,|=0 = |=0 = |=4 = |=5 = 0.|=0 = |=0 = |=2 = |=4 = 0.10.7. = 9D,10.19. = 4D,|=0 = (3 − )(5 − ), |=0 = 0,|=0 = (5 − )(4 − ), |=0 = 0,|=0 = |=0 = |=3 = |=5 = 0.|=0 = |=0 = |=5 = |=4 = 0.10.8. = 16D,10.20. = 9D,|=0 = (4 − )(6 − ), |=0 = 0,|=0 = (6 − )(5 − ), |=0 = 0,|=0 = |=0 = |=4 = |=6 = 0.|=0 = |=0 = |=6 = |=5 = 0.10.9.
= 25D,10.21. = 25D,|=0 = (5 − )(2 − ), |=0 = 0,|=0 = (2 − )(2 − ), |=0 = 0,|=0 = |=0 = |=5 = |=2 = 0.|=0 = |=0 = |=2 = |=2 = 0.10.10. = D,10.22. = D,|=0 = (6 − )(3 − ), |=0 = 0,|=0 = (3 − )(3 − ), |=0 = 0,|=0 = |=0 = |=6 = |=3 = 0.|=0 = |=0 = |=3 = |=3 = 0.10.11. = 9D,10.23. = 4D,|=0 = (2 − )(5 − ), |=0 = 0,|=0 = (4 − )(4 − ), |=0 = 0,|=0 = |=0 = |=2 = |=5 = 0.|=0 = |=0 = |=4 = |=4 = 0.10.12. = 16D,10.24.
= 9D,|=0 = (3 − )(6 − ), |=0 = 0,|=0 = (5 − )(5 − ), |=0 = 0,|=0 = |=0 = |=3 = |=6 = 0.|=0 = |=0 = |=5 = |=5 = 0.10.13. = 25D,10.25. = 16D,|=0 = (4 − )(2 − ), |=0 = 0,|=0 = (6 − )(6 − ), |=0 = 0,|=0 = |=0 = |=4 = |=2 = 0.|=0 = |=0 = |=6 = |=6 = 0.10.14. = D,10.26. = 144D,|=0 = (5 − )(3 − ), |=0 = 0,|=0 = (2 − )(7 − ), |=0 = 0,|=0 = |=0 = |=5 = |=3 = 0.|=0 = |=0 = |=2 = |=7 = 0.10.15. = 4D,10.27.
= 121D,|=0 = (6 − )(4 − ), |=0 = 0,|=0 = (3 − )(6 − ), |=0 = 0,|=0 = |=0 = |=6 = |=4 = 0.|=0 = |=0 = |=3 = |=6 = 0.10.16. = 16D,10.28. = 100D,|=0 = (2 − )(6 − ), |=0 = 0,|=0 = (4 − )(5 − ), |=0 = 0,|=0 = |=0 = |=2 = |=6 = 0.|=0 = |=0 = |=4 = |=5 = 0.10.17. = 25D,10.29. = 81D,|=0 = (3 − )(2 − ), |=0 = 0,|=0 = (5 − )(4 − ), |=0 = 0,|=0 = |=0 = |=3 = |=2 = 0.|=0 = |=0 = |=5 = |=4 = 0.10.18. = D,10.30. = 64D,|=0 = (4 − )(3 − ), |=0 = 0,|=0 = (6 − )(3 − ), |=0 = 0,|=0 = |=0 = |=4 = |=3 = 0.|=0 = |=0 = |=6 = |=3 = 0.10.31.
= 49D,|=0 = (7 − )(2 − ), |=0 = 0,|=0 = |=0 = |=7 = |=2 = 0.Задача 12. Найти решение первой смешанной краевой задачи для уравнения теплопроводностина отрезке.12.1. = 16 , 0 < < 3, > 0,⎧ 2⎨ , 0 6 6 3,2(, 0) = 3⎩3 − , 3 < 6 3,2(0, ) = (3, ) = 0.12.2. = , 0 < < 2, > 0,⎧⎨2 , 0 6 6 1,(, 0) =⎩2 − , 1 < 6 2,(0, ) = (2, ) = 0.12.3. = 25 , 0 < < 5, > 0,⎧ 2⎨ 2 , 0 6 6 5 ,52(, 0) =⎩5 − , 5 < 6 5,2(0, ) = (5, ) = 0.12.4.