Consider the function $f(x,t)=sin(x-ct)$ where $c$ is a constant. Calculate $\frac{de{l}^{2}f}{del{x}^2}$ and $\frac{de{l}^{2}f}{del{t}^2}.$

$\frac{de{l}^{2}f}{del{x}^2}=$

$$

The one$-$dimensional wave equation is given by $\frac{de{l}^{2}f}{del{x}^2}=\frac{1}{c^2}\frac{de{l}^{2}f}{del{t}^2}$ and the one$-$dimensional heat equation is given by $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{t}}=c^2\frac{de{l}^{2}f}{del{x}^2}.$ What can be said about $f?$

$f$ satisfies the one$-$dimensional heat equation.