a) Use the formula eq2 dq = to show that the solution of the heat equation ut = kuxx on the real line, < x < , with initial condition u(x, 0) = 1 is u(x, t) = 1 for all x R and t > 0 . (b) Prove the result in (a) by finding a particular solution of the same IVP and using the well-posedness of the IVP for the heat equation