A thin wire coinciding with the x-axis on the interval [-L, L] is bent into the shape of a circle so that the ends x = -L and x = L are joined. Under certain conditions, the temperature u(x, t) in the wire satisfies the boundary-value problem кози 8x2 7 = au -L<x<L,t > 0, at' u(-L, t)u(L, t), t> 0. ди ขน = t> 0 дх дх x= -L x = L u(x, 0) = f(x), -L <x<L. Find the temperature u(x, t). L u(x, t) = (f(x) dx)( [ 2L 00 - Σ n = 1 L f(x) cos(x) dx) ( +( f(x) sin (IX) dx) (