Consult any standard engineering mathematics book and solve the following PDE analytically:

\[
\begin{equation*}
\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0 \tag{11.105}
\end{equation*}
\]

The boundary conditions are given by

\[
\begin{equation*}
u(x=0)=u_{1}, u\left(x=L_{x}ight)=u_{2}, u(y=0)=u_{3}, u\left(y=L_{y}ight)=u_{4} \tag{11.106}
\end{equation*}
\]

where, \(u_{1}, u_{2}, u_{3}\) and \(u_{4}\) are constants.