\fConsider the one-dimensional wave equation at2 = 100 2x2 ' on the interval [0, 10], subject to the boundary conditions u(0, t) = 0 and u(10, t) = 0, t > 0. (i) Show that a solution u(x, t) can be written as OO nTIX u(x, t) = > (Bn cos(nut) + B* sin(nut)) sin 10 n=1