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Let u be the solution to the initial boundary value problem for the Heat Equation, dzu(t, x) = 4 0?u(t, x), t e (0, 0), хе (0, 3)%; with Dirichlet boundary conditions u(t, 0) = 0 and u(t, 3) = 0, and with initial condition ze [0, 4). 0, u (0, г) — f(z) —- 2, 0, The solution u of the problem above, with the conventions given in class, has the form u(t, x) = Cn Vn (t) Wn(x), n=1 with the normalization conditions v, (0) =1 and wn = 1. Find the functions v,, Wn, and the constants Cn: Vn (t) Σ Wn(x) = Σ Cn = Σ

Let u be the solution to the initial boundary value problem for the Heat Equation, dzu(t, x) = 4 0?u(t, x), t e (0, 0), хе (0, 3)%; with Dirichlet boundary conditions u(t, 0) = 0 and u(t, 3) = 0, and with initial condition ze [0, 4). 0, u (0, г) — f(z) —- 2, 0, The solution u of the problem above, with the conventions given in class, has the form u(t, x) = Cn Vn (t) Wn(x), n=1 with the normalization conditions v, (0) =1 and wn = 1. Find the functions v,, Wn, and the constants Cn: Vn (t) Σ Wn(x) = Σ Cn = Σ

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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Let u be the solution to the initial boundary value problem for the Heat Equation, dzu(t, x) = 4 0?u(t, x), t e (0, 0), хе (0, 3)%; with Dirichlet boundary conditions u(t, 0) = 0 and u(t, 3) = 0, and with initial condition ze [0, 4). 0, u (0, г) — f(z) —- 2, 0, The solution u of the problem above, with the conventions given in class, has the form u(t, x) = Cn Vn (t) Wn(x), n=1 with the normalization conditions v, (0) =1 and wn = 1. Find the functions v,, wn, and the constants Cn: Vn (t) Σ Wn(x) = Σ Cn = Σ
Transcribed Image Text:Let u be the solution to the initial boundary value problem for the Heat Equation, dzu(t, x) = 4 0?u(t, x), t e (0, 0), хе (0, 3)%; with Dirichlet boundary conditions u(t, 0) = 0 and u(t, 3) = 0, and with initial condition ze [0, 4). 0, u (0, г) — f(z) —- 2, 0, The solution u of the problem above, with the conventions given in class, has the form u(t, x) = Cn Vn (t) Wn(x), n=1 with the normalization conditions v, (0) =1 and wn = 1. Find the functions v,, wn, and the constants Cn: Vn (t) Σ Wn(x) = Σ Cn = Σ
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