I1

Please show your work and answer ALL PARTS.

Additional exercise 3): Consider the wave equation azu at2 where c is a positive constant. (i) For each u > 0, the function cos(cut) cos(ux) is a solution of the wave equation. Please find explicit functions F() and G(n) such that cos(cut) cos(ux) = F(a + ct) + G(x - ct). (ii) For each / > 0, the function sin(cut) cos(ux) is a solution of the wave equation. Please find explicit functions F($) and G(n) such that sin(cut) cos(ux) = F(x + ct) + G(x - ct)