4.3 Find the solution subject to the following boundary and initial conditionsof the wave equation, utt = a²uxx-(a) u(0, t) = u(r, t) = 0, u(x,0) = sin(x), u₂(x,0) = 0(b) u(0, t) = u(1, t) = 0, u(x,0) = x(1-x), ut(x, 0) = sin(x)if 0≤x≤n,t> 0Utt-4uxx=0(c)u(r,0) = 3 cos (r), u₂(x,0) = 1 - cos(4x)u₂(0, t) = u(n, t) = 0Utt-c²Uzz = 0(d)u(0,t) = 0, u, (1, t) = cos(t)(u(x,0) = u₂(x,0) = 0if 0≤x≤ 1,t> 0

(a) Given utt=α2uxx ux,0=sinx, ut(0,t)=0 Using D' Alembert formula, we know for the wave equation…

Answered: 4.3 Find the solution subject to the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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