5. let u(x, t) be the temperature of a bar of length 10, at position x and time t (in hours). suppose that the left endpoint of the bar is not insulated, but the right endpoint is fully insulated, and the bar is sitting in a 70◦ room. moreover, suppose that initially, the temperature increases linearly from 70◦ at the left endpoint to 80◦ at the other end. finally, suppose the interior of the bar is poorly insulated, so heat can escape. (a) suppose that heat escapes at a constant rate of 1◦ per hour. write (but do not solve) an initial/boundary value problem for u(x, t) that could model this situation. (b) a more realistic situation would be for heat to escape not at a constant rate, but at a rate proportional to the difference between the temperature of the bar and the ambient temperature of the room. write an initial/boundary value problem for u(x, t) that could model this situation. what is the steady-state solution and why?