This one-way wave equation can be solved by interpreting it as telling us that the directional derivative of v in the (1, -c) direction is 0. This means that the value of v is constant on characteristic lines of the form x + ct = x 0, and thus that v must depend only on x + ct, that is, have the form H (x + ct). Then, to solve the first (inhomogenous) one-way wave equation relating v to u, we can note that its homogenous solution must be a function of the form F (x - ct), by logic similar to the above. Guessing a particular solution of the form G (x + ct), we find that