This means we can find a particular solution G of the desired form by integration. Thus, we have again shown that u obeys u (x, t) = F (x - ct) + G (x + ct) via one-way wave equations. Note that since the one-way wave differential operators commute for analytic functions by Clairaut's theorem, we could have equivalently set up our system of one-way wave equations so that we solved them in the opposite order.