Solve the one-dimensional heat equation below with a time-dependent heat source and non-homogeneous boundary conditions: 7. Ut = Uxx + Q(x,t) ВС: и(0, t) — 1, и(п,t) — 0 u(x, 0) = (x + 7)(T – x), IC : where a) Q(х, t) —D е-t sin 3x — e-21 sin 4t b) Q(x, t) = e-3t sin 5x.

Solve the one-dimensional heat equation below with a time-dependent heat source and non-homogeneous boundary conditions: 7. Ut = Uxx + Q(x,t) ВС: и(0, t) — 1, и(п,t) — 0 u(x, 0) = (x + 7)(T – x), IC : where a) Q(х, t) —D е-t sin 3x — e-21 sin 4t b) Q(x, t) = e-3t sin 5x.

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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Question

Solve the one-dimensional heat equation below with a time-dependent heat source and non-homogeneous
boundary conditions:
7.
Ut = Uxx + Q(x,t)
ВС: и(0, t) — 1, и(п,t) — 0
IC : u(x,0) –(r +7)(T – x),
where
а) Qх, t) — е'sin 3x — e -2t sin 4t
b) Q(х, t) — е 3' sin 5x.

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