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Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 50/u(t, x), t≤ (0,∞), x = (0,3); with Dirichlet boundary conditions u(t,0) = 0 and u(t, 3) = 0, and with initial condition 3 u(0, x) = f(x) x, 0, with the normalization conditions v₁ (0) = 1 and wn x E x E 3 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 = 1. Find the functions vn, wn, and the constants Cn.

Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 50/u(t, x), t≤ (0,∞), x = (0,3); with Dirichlet boundary conditions u(t,0) = 0 and u(t, 3) = 0, and with initial condition 3 u(0, x) = f(x) x, 0, with the normalization conditions v₁ (0) = 1 and wn x E x E 3 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 = 1. Find the functions vn, wn, and the constants Cn.

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, du(t, x) = 5 d²u(t, x), t≤ (0, ∞), x = (0,3); 0 and u(t, 3) = 0, and with initial condition with Dirichlet boundary conditions u(t,0) = u(0, x) = f(x) u(t, x) = = with the normalization conditions vn (0) = 1 and wn (2³2) ∞ x, The solution u of the problem above, with the conventions given in class, has the form n=1 0, = [0, ³²), 3 x = x E en vn (t) wn(x), = 1. Find the functions vn, wn, and the constants Cn.
Transcribed Image Text:Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 5 d²u(t, x), t≤ (0, ∞), x = (0,3); 0 and u(t, 3) = 0, and with initial condition with Dirichlet boundary conditions u(t,0) = u(0, x) = f(x) u(t, x) = = with the normalization conditions vn (0) = 1 and wn (2³2) ∞ x, The solution u of the problem above, with the conventions given in class, has the form n=1 0, = [0, ³²), 3 x = x E en vn (t) wn(x), = 1. Find the functions vn, wn, and the constants Cn.
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