Propagation of heat in a laterallyr insulated 10 Length L = 1m Thermal diffusivity {I = 0:23 cmz/s At time t = 0, bar temperature u(x,0) = x (L-x), where x is the coordinate along the bar axis. The extremities of the bar are kept at temperature u_(0; t) = u(L; t) = 0. The distribution of temperature is: all\": t) = g B\" sin (71:11:) adoErr} (1} - Show that this distribution satisfies the heat equation. substitute the solution [1) into (2) and check that the identity is satisfied. 2 E=Cau 3t 83:2 I l2)