Consider the standard equilibrium heat equation u_t = 0 = u_xx on x element [0, 1]. given the following parameter values and boundary conditions, determine (1) the equilibrium solution and draw a graph, and (2) compute the flux phi and indicate on the solution graph the direction and magnitude of the flux. alternatively, specify if the solution does not exist or is not fully determined. (a) u (0) = 10, u (1) = 21. (b) u (0) = 2, u' (0) = 0. (c) u' (0) = 4, u (1) = 0. (d) u' (0) = 3, u'(1) = 3. (e) u' (0) = 10, u'(1) = 0. (f) u (0) = u (1), u' (0) = u' (1).