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3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 00 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 00 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x

3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 00 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 00 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x

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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Please solve the following by hand and without the use of AI. Please be thorough and use detailed mathematical formulas to solve. Thank you.

3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x <L/2 1, x L/2. = when f(x)=
Transcribed Image Text:3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x <L/2 1, x L/2. = when f(x)=
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