Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 2 / 6 / Solution

Expanding gives $u=2x^2+2c^2{t}^2$, so $u_{tt}=4c^2$ and $u_{xx}=4$. Hence $u_{tt}=c^2{u}_{xx}$, proving that it solves the one-dimensional wave equation. Equivalently its two summands are oppositely travelling profiles, as in D'Alembert's formula.