22. Solve the following Dirichlet problems:V²u = 0,(a)0 < x < 1,0 < y < 1,u (x, 0) = x (x – 1) ,u (x, 1) = 0,0 < x< 1,u (0, y) = 0,и (1, у) — 0,0 < y< 1.(d)V²u = 0,0 < x < 1,0 < y < 1,и (х, 0) %3D 0,u (x, 1) = 0,0 < x < 1,u (0, y) = 0,u (1, y) = sin TY COS TY,0

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Answered: 22. Solve the following Dirichlet…

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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22. Solve the following Dirichlet problems: (a) V²u = 0, u (x,0) = x (x - 1), u (0, y) = 0, 0 < x < 1, u (x, 1) = 0, u (1, y) = 0, 0 < y < 1, 0≤x≤ 1, 0 ≤ y ≤ 1.