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It was shown in lectures that the wave equation 22 и at2 = a²u c2 8x2' u(0,t) = 0, u(L,t) = 0, has general solution u(x,t) = = ппх nπct nπct sin an COS + bn sin L L L n=1 Explicitly find the coefficients an and bn for the following initial value problems (a) u(x,0) = x(L− x), u(x, 0) = 0, (b) u(x,0) = 0, u(x,0) = x(L − x).

It was shown in lectures that the wave equation 22 и at2 = a²u c2 8x2' u(0,t) = 0, u(L,t) = 0, has general solution u(x,t) = = ппх nπct nπct sin an COS + bn sin L L L n=1 Explicitly find the coefficients an and bn for the following initial value problems (a) u(x,0) = x(L− x), u(x, 0) = 0, (b) u(x,0) = 0, u(x,0) = x(L − 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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It was shown in lectures that the wave equation 22 и Ət² a² u u(0,t) = 0, u(L,t) = 0, 8x2' has general solution ∞ u(x,t) = Σ sin n=1 ППХ L (a nπct nπct an COS + bn sin L L Explicitly find the coefficients an and bn for the following initial value problems ди (a) u(x, 0) = x(L-x), u(x, 0) = 0, ди Ət (b) u(x, 0) = 0, (x, 0) = x(L − x).
Transcribed Image Text:It was shown in lectures that the wave equation 22 и Ət² a² u u(0,t) = 0, u(L,t) = 0, 8x2' has general solution ∞ u(x,t) = Σ sin n=1 ППХ L (a nπct nπct an COS + bn sin L L Explicitly find the coefficients an and bn for the following initial value problems ди (a) u(x, 0) = x(L-x), u(x, 0) = 0, ди Ət (b) u(x, 0) = 0, (x, 0) = x(L − x).
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