The Ends of a Rod 40 Cm in Length Are

Multiple Choice

The ends of a rod 40 cm in length are connected to reservoirs that maintain the temperature at 12°C at x = 0 and 14°C at x = 40. The initial boundary value problem governing how heat conducts through the rod is as follows:

What is the solution u(x, t) of the initial boundary value problem?

A) u(x, t) = v(x) * w(x, t)
B) u(x, t) = v(x) + w(x, t) + C, where C is an arbitrary real constant.
C) u(x, t) = v(x) + w(x, t)
D) u(x, t) = w(x, t) - v(x)