Consider the wave equation Ju x u t c where c is a positive constant. (i) For each > 0, the function cos(cut) cos(x) is a solution of the wave equation. Please find explicit functions F() and G(n) such that cos(ct) cos(x) = F(x + ct) + G(x ct). = (ii) For each > 0, the function sin(ct) cos(x) is a solution of the wave equation. Please find explicit functions F() and G(n) such that sin(cut) cos(x) = F(x + ct) +G(x ct). =