(3) A dynamical system is governed by two equations: = y, y = In(x' + y)-3y. Here a dot on the top of a symbol stands for the derivative with respect to t. (a) Find critical points of this system. (b) Using linearisation of the system in the neighbourhood of each critical point, determine the nature of the critical points. (c) Draw qualitatively but neatly these critical points and corresponding trajectory diagrams. (4) the functional F[y] = ] [(y) -x3 + 4ye x x such that y(0) = y(x/2) = 0. Calculate the minimal value of the functional Fly]