Consider a metal rod (0 < x < l), insulated along its sides but not at its ends, which is initially at temperature = 1. Suddenly both ends are plunged into a bath of temperature = 0. Write the differential equation, boundary conditions (take Dirichlet), and the initial condition. Write the formula for the temperature u(x, t) at later times. Your answer should involve neither R nor (·, ·)L2 symbols. Use the infinite series expansion of the initial datum 1 = 4 π sin πx l + 1 3 sin 3πx l + 1 5 sin 5πx l + · · ·