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

\[
\begin{equation*}
\frac{\partial u}{\partial t}=\alpha \frac{\partial^{2} u}{\partial x^{2}} \tag{11.103}
\end{equation*}
\]

Initial and boundary conditions are given by

\[
\begin{equation*}
u(t=0)=u_{0}(x) ; u(x=0)=u_{1}, u(x=L)=u_{2} \tag{11.104}
\end{equation*}
\]

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