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Find the generalized solution to the following heat equation ди a(x)- dt ди (7(x)) – B(x)u, 0 0, | дх dx

Find the generalized solution to the following heat equation ди a(x)- dt ди (7(x)) – B(x)u, 0 0, | дх dx

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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Show me step by step this question posted before dont copy that I dont need that. Make sure use Laplaces's equation

 

Use : Laplaces's equation to solve this question 

Find the generalized solution to the following heat equation ди ди a(x)- dt T(x)- — В(х)и, 0 < x < 1, t> 0, dx дх ди aj u(0, t) + ß1(0, t) = 0, t> 0, dx ди azu(1, t) + B2(1, t) = 0, t> 0, u(x,0) = f(x), 0<x<1, where 1. a(x) > 0, t(x) > 0, B(x) > 0 for 0 < x < 1, 2. a1, a2, Bi, B2 are real valued, af + B; # 0 and af + B? # 0.
Transcribed Image Text:Find the generalized solution to the following heat equation ди ди a(x)- dt T(x)- — В(х)и, 0 < x < 1, t> 0, dx дх ди aj u(0, t) + ß1(0, t) = 0, t> 0, dx ди azu(1, t) + B2(1, t) = 0, t> 0, u(x,0) = f(x), 0<x<1, where 1. a(x) > 0, t(x) > 0, B(x) > 0 for 0 < x < 1, 2. a1, a2, Bi, B2 are real valued, af + B; # 0 and af + B? # 0.
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