диa²uWhen solving the heat equationatfor 0 0, with8.əx2boundary conditions and initial condition:u(0, t) = u(1, t) = 0for t> 0и(х, 0) 3D 1 — 2хfor 0

Given heat equation is ∂u∂t=∂2u∂x2 (1) with initial and boundary condition is:…

When solving the heat equation n,e for 0 0, with 8. пе at boundary conditions and initial condition: u(0, t) = u(1,t) = 0 for t> 0 и(х, 0) — 1 — 2х for 0 Bne-(nn)?t; *sin(nnx) n=1 Continue from here to solve the temperature u(x, t).

When solving the heat equation n,e for 0 0, with 8. пе at boundary conditions and initial condition: u(0, t) = u(1,t) = 0 for t> 0 и(х, 0) — 1 — 2х for 0 Bne-(nn)?t; *sin(nnx) n=1 Continue from here to solve the temperature u(x, t).

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

ди
a²u
When solving the heat equation
at
for 0<x < 1 and t> 0, with
8.
əx2
boundary conditions and initial condition:
u(0, t) = u(1, t) = 0
for t> 0
и(х, 0) 3D 1 — 2х
for 0<x < 1,
after applying separation of variables and boundary conditions, you found a solution of the form:
00
и(х, t)
B,e-(nn)*t sin(nnx)
n=1
Continue from here to solve the temperature u(x,t).

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