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) Find the solution of the two-dimensional Laplace equation

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(40 marks) Find the solution of the two-dimensional Laplace equation

$$ u_{x x}+u_{y y}=0 \quad 0<x<1,0<y<1 $$

with the boundary conditions

$$ u(x, 1)=x, u(x, 0)=u(0, y)=0, u(1, y)=y $$

mathematics   physics   Partial-Differential-Equations   Differential-Equations   
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