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Find w(r, t) in the form of Fourier sine series over 0 < I<: w(r, t) = [w.(t) sin(nz) 0

Find w(r, t) in the form of Fourier sine series over 0 < I<: w(r, t) = [w.(t) sin(nz) 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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Hand written plz asap.... Fast plz asap solve b part only...

where q(r, t) = (DE) (BC) (IC) Consider the following initial-boundary value problem: dw Fw Ət əx² w(0, t) = 0, w(π, t) = 0 w(1,0) = g(1), 8 g(x, t) = 2(T-x)e-²¹, g(x) = x-n. (a) Expand g(x, t) and g(r) in Fourier sine series over 0 < I<T: n=1 + g(x,t) n(t) sin(nx) 0<x< ^, 0<x<,t> 0, t> 0, 0<I<T, DO g(x) = [gn sin(nr) 0<I<1. 71001 Find qn(t) and 9n- (b) Find w(r, t) in the form of Fourier sine series over 0) < I<*: w(r, t) = w. (t) sin(n) 0<x<*.
Transcribed Image Text:where q(r, t) = (DE) (BC) (IC) Consider the following initial-boundary value problem: dw Fw Ət əx² w(0, t) = 0, w(π, t) = 0 w(1,0) = g(1), 8 g(x, t) = 2(T-x)e-²¹, g(x) = x-n. (a) Expand g(x, t) and g(r) in Fourier sine series over 0 < I<T: n=1 + g(x,t) n(t) sin(nx) 0<x< ^, 0<x<,t> 0, t> 0, 0<I<T, DO g(x) = [gn sin(nr) 0<I<1. 71001 Find qn(t) and 9n- (b) Find w(r, t) in the form of Fourier sine series over 0) < I<*: w(r, t) = w. (t) sin(n) 0<x<*.
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