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(a) (b) (c) U₁=zUxx+f, 0≤x≤1,t€R+ if fo f(x) dx = 0. ux(0,1)=0=ux(1,1), 1€R+ lim_max |u(x, t)| = 0 1+0 0≤x≤1 What happens if fo f(x)dx=0?

(a) (b) (c) U₁=zUxx+f, 0≤x≤1,t€R+ if fo f(x) dx = 0. ux(0,1)=0=ux(1,1), 1€R+ lim_max |u(x, t)| = 0 1+0 0≤x≤1 What happens if fo f(x)dx=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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homework practice, this class is about Fourier series; generalized functions; and numerical methods.

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5. Show that the solution (b) 00 u(x,t) = 2 Σ n=1 satisfies the following three conditions (a) (c) (1-6-21/2) [ƒ(y) cos (nty)dy cos (næx) e (π²n²/2) 1 U₁=₂Uxx+f, 0≤x≤1,1€R+ if fo f(x) dx = 0. ux(0,1)=0=ux(1,1), 1ER+ lim max |u(x,t) = 0 1-0 0≤x≤1 What happens if fo f(x) dx ‡0?
Transcribed Image Text:5. Show that the solution (b) 00 u(x,t) = 2 Σ n=1 satisfies the following three conditions (a) (c) (1-6-21/2) [ƒ(y) cos (nty)dy cos (næx) e (π²n²/2) 1 U₁=₂Uxx+f, 0≤x≤1,1€R+ if fo f(x) dx = 0. ux(0,1)=0=ux(1,1), 1ER+ lim max |u(x,t) = 0 1-0 0≤x≤1 What happens if fo f(x) dx ‡0?
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