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Find a formal solution to the following initial-boundary value problem. du = 3- at 0 0, - du (0,t) = 0, u(a,t) = 0 t>0, u(x,0) = f(x), 0

Find a formal solution to the following initial-boundary value problem. du = 3- at 0 0, - du (0,t) = 0, u(a,t) = 0 t>0, u(x,0) = f(x), 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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Find a formal solution to the following initial-boundary value problem. du = 3- 0 <x< T, t>0, - du (0,t) = 0, u(T, t) = 0 dx t>0, u(x,0) = f(x), 0<x<T With u(x,t) = X(x)T(t), what is the associated boundary value problem for X(x)? A. X(x)– 1X(x) = 0, X'(0) = X(0) = 0 B. X"(x) + 2X(x) = 0, X'(0) = X(x) = 0 C. X"(x) + AX(x) = 0, X'(0) = X(0) = 0 D. X"(x)– 1X(x) = 0, X'(0) = X(x) = 0
Transcribed Image Text:Find a formal solution to the following initial-boundary value problem. du = 3- 0 <x< T, t>0, - du (0,t) = 0, u(T, t) = 0 dx t>0, u(x,0) = f(x), 0<x<T With u(x,t) = X(x)T(t), what is the associated boundary value problem for X(x)? A. X(x)– 1X(x) = 0, X'(0) = X(0) = 0 B. X"(x) + 2X(x) = 0, X'(0) = X(x) = 0 C. X"(x) + AX(x) = 0, X'(0) = X(0) = 0 D. X"(x)– 1X(x) = 0, X'(0) = X(x) = 0
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