Solving potential equation ODE Solve completely for u(x,y) given thatO²u(x,y) , ô²u(x,y)ôy?for 0 < x < a and 0 < y < b, and the boundary conditionsди(х,у)u(0,y)1Əxx=afor 0 < y < b, andди(х, у)дуu(x,b)1y=0for 0 < x < a.

We need to solve completely u(x, y) for the following system.…

Solve completely for u(x,y) given that a²u(x,v) ô²u(x,y) + %3D Ôx? ôy? for 0 < x < a and 0 < y < b, and the boundary conditions ди(х, у) u(0,y) = 1 %3D x=a for 0 < y < b, and ди(х, у) u(x,b) = 1 %3D y-0 for 0

Solve completely for u(x,y) given that a²u(x,v) ô²u(x,y) + %3D Ôx? ôy? for 0 < x < a and 0 < y < b, and the boundary conditions ди(х, у) u(0,y) = 1 %3D x=a for 0 < y < b, and ди(х, у) u(x,b) = 1 %3D y-0 for 0

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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Question

Solving potential equation ODE

Solve completely for u(x,y) given that
O²u(x,y) , ô²u(x,y)
ôy?
for 0 < x < a and 0 < y < b, and the boundary conditions
ди(х,у)
u(0,y)
1
Əx
x=a
for 0 < y < b, and
ди(х, у)
ду
u(x,b)
1
y=0
for 0 < x < a.

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