The characteristics of a partial differential equation are defined as lines along which information is transported. For a differential equation of the form A \frac{\partial^{2} \phi}{\partial x^{2}}+2 B \frac{\partial^{2} \phi}{\partial

x \partial y}+D \frac{\partial^{2} \phi}{\partial y^{2}}=f\left(x, y, \frac{\partial \phi}{\partial x}, \frac{\partial \phi}{\partial x}\right) the characteristics are given by the solutions of the equation A\left(\frac{d y}{d x}\right)^{2}-2 B\left(\frac{d y}{d x}\right)+D=0 Find the characteristics of the wave equation and draw a picture of these on the xt-plane. Hint: Think of Eq. 5 as a quadratic; solve it and integrate the result. Explain the statement "characteristics of a partial differential equation are defined as lines along which information is transported" by considering the relationship between the coordinates (n, E) and the characteristics?