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B.C.: In Problems 7-15, solve the given heat conduction 7. u = a ²u₁, 8. B.C.: u(0, 1) = 1, I.C.: u(x, 0) = 1 + x 9. Uxx = a ²u₁, 11. 00 u.(p, t) = 0 00 1>0 u(p, t) = To 0 < x < 1, 1>0 1>0 u(1, 1) = To u(x, 0) = To + x(1-x) *12. u = a 2u₁, 0 < x < 1, 1>0 B.C.: u(0, t) = T₁, u,(1, 1) = 0 I.C.: u(x, 0) = x 13. u = a 2u₁, -TT < X < T, B.C.: u(-, t) = u(n, t), I.C.: u(x, 0) = |x| 14. u = a 2u₁, 0 < x < 1, t>0 u.(-π, t) = u₂(π, t) t> 0

B.C.: In Problems 7-15, solve the given heat conduction 7. u = a ²u₁, 8. B.C.: u(0, 1) = 1, I.C.: u(x, 0) = 1 + x 9. Uxx = a ²u₁, 11. 00 u.(p, t) = 0 00 1>0 u(p, t) = To 0 < x < 1, 1>0 1>0 u(1, 1) = To u(x, 0) = To + x(1-x) *12. u = a 2u₁, 0 < x < 1, 1>0 B.C.: u(0, t) = T₁, u,(1, 1) = 0 I.C.: u(x, 0) = x 13. u = a 2u₁, -TT < X < T, B.C.: u(-, t) = u(n, t), I.C.: u(x, 0) = |x| 14. u = a 2u₁, 0 < x < 1, t>0 u.(-π, t) = u₂(π, t) t> 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8 and 11 question please
В.С.: и(0, 1) In Problems 7-15, solve the given heat conduction problem. 7. u = a²u,, В.С.: и(0, 1) - 1, и(1, 1) 3 0 I.C.: и(х, 0) - 1 + х 0<x< 2, U = a?u, В.С.: и(0, г) - Т,, и(х, 0) 3D То 8. и(2, г) 3 Т, I.C.: 9. u= au,, 0<x<p, t>0 В.С.: и,(0, г) %3D 0, u(x, 0) = T, sin'(x/p) и, (р, 1) %3D 0 I.C.: 10. u = a-u,, В.С.: и,(0, 1) %3D 0, и(х, 0) - То 0<x <p, u(p, 1) = To I.C.: 0<x < 1, 11. u = a²u,, В.С.: и(0, г) 3D То, t>0 и(1, 1) %3D То I.C.: и(х, 0) - То + x(1 -х) *12. u = a u, 0 <x < 1, и, (1, г) 3 0 t>0 В.С.: и(0, г) T, %3D I.C.: и(х, 0) - х 13. U = a?u,, В.С.: и(-п, 1) %3D и(п, 1), I.C.: u(x, 0) = |x| - T <x< T, t>0 u,(- T, 1) = u,(, 1) 14. U = a?u, В.С.: и(0, 1) %3D 0, 0 <x < 1, t>0 2u(1, 0) + и,(1, 1) %3D 0 I.C.: и(х, 0) %3D Т
Transcribed Image Text:В.С.: и(0, 1) In Problems 7-15, solve the given heat conduction problem. 7. u = a²u,, В.С.: и(0, 1) - 1, и(1, 1) 3 0 I.C.: и(х, 0) - 1 + х 0<x< 2, U = a?u, В.С.: и(0, г) - Т,, и(х, 0) 3D То 8. и(2, г) 3 Т, I.C.: 9. u= au,, 0<x<p, t>0 В.С.: и,(0, г) %3D 0, u(x, 0) = T, sin'(x/p) и, (р, 1) %3D 0 I.C.: 10. u = a-u,, В.С.: и,(0, 1) %3D 0, и(х, 0) - То 0<x <p, u(p, 1) = To I.C.: 0<x < 1, 11. u = a²u,, В.С.: и(0, г) 3D То, t>0 и(1, 1) %3D То I.C.: и(х, 0) - То + x(1 -х) *12. u = a u, 0 <x < 1, и, (1, г) 3 0 t>0 В.С.: и(0, г) T, %3D I.C.: и(х, 0) - х 13. U = a?u,, В.С.: и(-п, 1) %3D и(п, 1), I.C.: u(x, 0) = |x| - T <x< T, t>0 u,(- T, 1) = u,(, 1) 14. U = a?u, В.С.: и(0, 1) %3D 0, 0 <x < 1, t>0 2u(1, 0) + и,(1, 1) %3D 0 I.C.: и(х, 0) %3D Т
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