The general solution for Uxx + Uyy = 0, u(x, 0) = 1, u(x, ) =...

 

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The general solution for Uxx + Uyy = 0, u(x, 0) = 1, u(x, π) = 0, u(0, y) = 0, u(л, y) = 0 is Σlaney+bne-n*y] sin(nxx) Olanex+bne "x] sin(ny) [an sin(nx) + b₂ cos(-nx)] sin(ny) n=1 Olan sin(nxx) + bn cos(-nxx)] sin(ny) Σlaney + beny] sin(nx) Olan sin(nxx) + bn cos(-nxx)] sin(nxy) Σlane*x + b₂e-"**] sin(ny) O[an, sin(ny) + b, cos(-ny)] sin(nx) 100 The general solution for Uxx + Uyy = 0, u(x, 0) = 1, u(x, π) = 0, u(0, y) = 0, u(л, y) = 0 is Σlaney+bne-n*y] sin(nxx) Olanex+bne "x] sin(ny) [an sin(nx) + b₂ cos(-nx)] sin(ny) n=1 Olan sin(nxx) + bn cos(-nxx)] sin(ny) Σlaney + beny] sin(nx) Olan sin(nxx) + bn cos(-nxx)] sin(nxy) Σlane*x + b₂e-"**] sin(ny) O[an, sin(ny) + b, cos(-ny)] sin(nx) 100

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son Given Given Uxx with ux y1u x 1 0 y 0 u 17 y Let ux y x x 4 9 uxx ... View the full answer