1. Find the solution of the wave equationa² uƏt²[ a² u.c²მ2 მy2+0 < x <1, 0 < y < 1with the boundary conditionsu = 0, x = 0,1ди= 0, y = 0,1მყand the initial conditions u(x, y, 0) = x(1 − x)y and ut(x, y, 0) = 0.

Answer Explanation:Step 1: Step 2: Step 3: Step 4:

Answered: 1. Find the solution of the wave…

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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1. Find the solution of the wave equation a² u Ət² [ a² u . c² მ2 მy2 + 0 < x <1, 0 < y < 1 with the boundary conditions u = 0, x = 0,1 ди = 0, y = 0,1 მყ and the initial conditions u(x, y, 0) = x(1 − x)y and ut(x, y, 0) = 0.