[See] Solve the Laplace equation with the following boundary conditions. u_xx+u_yy=0, 0≤ x≤ a,0≤ y≤ b , u(x,0)=f(x), u(x,b)=g(x), u(0,y)=0,
Question: Solve the Laplace equation with the following boundary conditions.
\[\begin{aligned} & {{u}_{xx}}+{{u}_{yy}}=0,\quad 0\le x\le a,0\le y\le b \\ & u(x,0)=f(x),\,\,\,u(x,b)=g(x),\,\,\,u(0,y)=0,\,\,\,u(a,y)=0 \\ \end{aligned}\]
(Hint: Write the solution as the sum of the solutions of two different boundary value problems for the Laplace equation).
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