Solve using separation of variables.

An insulated uniform metal bar, 8m long, has the temperature of its ends maintained at O C, and at time t=0 the temperature distribution f(x) along the bar is defined by f (x) = x(8 -x). If c2 = 1. solve the heat con- 22 u 1 du duction equation to determine 2x2 c2 at the temperature u at any point in the bar at time t