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(e) Given that the general solution of the partial differential equation and boundary conditions may be expressed as (2η 1)ππ -ΣC₁ exp(-D(2n=1³4²¹) com (2n = 1)*²) COS 2L n=1 θ(x,t) = Σ Cn exp find the particular solution that satisfies the given initial temperature distribution.

(e) Given that the general solution of the partial differential equation and boundary conditions may be expressed as (2η 1)ππ -ΣC₁ exp(-D(2n=1³4²¹) com (2n = 1)*²) COS 2L n=1 θ(x,t) = Σ Cn exp find the particular solution that satisfies the given initial temperature distribution.

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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The temperature distribution 0(x, t) along an insulated metal rod of length L is described by the differential equation 2²0 1 00 əx² D Ət 0(x,0) = 0.3 cos (0<x<L, t> 0), where D0 is a constant. The rod is held at a fixed temperature of 0°C at one end and is insulated at the other end, which gives rise to the boundary L for conditions = 0 when x = 0 for t> 0 together with 0 = 0 when x = t> 0. 20 əx The initial temperature distribution in the rod is given by là coitulos (0 ≤ x ≤ L). (17) 2 L (2 in U dram 1 upe
Transcribed Image Text:The temperature distribution 0(x, t) along an insulated metal rod of length L is described by the differential equation 2²0 1 00 əx² D Ət 0(x,0) = 0.3 cos (0<x<L, t> 0), where D0 is a constant. The rod is held at a fixed temperature of 0°C at one end and is insulated at the other end, which gives rise to the boundary L for conditions = 0 when x = 0 for t> 0 together with 0 = 0 when x = t> 0. 20 əx The initial temperature distribution in the rod is given by là coitulos (0 ≤ x ≤ L). (17) 2 L (2 in U dram 1 upe
(e) Given that the general solution of the partial differential equation and boundary conditions may be expressed as (2η - 1)πα D(2n-1)²²t\ bahw 4L² 2L 11 nobon find the particular solution that satisfies the given initial temperature distribution. [C₁ exp(- 7²4). COS alni no n=1 0(x,t) = Σ Cn exp TI
Transcribed Image Text:(e) Given that the general solution of the partial differential equation and boundary conditions may be expressed as (2η - 1)πα D(2n-1)²²t\ bahw 4L² 2L 11 nobon find the particular solution that satisfies the given initial temperature distribution. [C₁ exp(- 7²4). COS alni no n=1 0(x,t) = Σ Cn exp TI
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