Famous PDEs
In the Natural Sciences we often encounter problems with many variables
constrained by boundary conditions and initial values. Many of these problems
can be modelled as partial differential equations. One case which arises
in many situations is the so-called wave equation whose one-dimensional form
reads
$$
\begin{equation}
\tag{1}
\frac{\partial^2 u}{\partial x^2}=A\frac{\partial^2 u}{\partial t^2},
\end{equation}
$$
where \( A \) is a constant. The solution \( u \) depends on both spatial and temporal variables, viz. \( u=u(x,t) \).