4. (a) Find the solution to dy1 = 391 - 92 dt dy2 = 12 + 3y1 dt with the initial condition y1 (0) = 3, y2 (0) = 0. Sketch this solution on a phase diagram. (b) Find the general solution for the system i =9x - 7y + 3z y = 12x - 10y + 3z 2 = 16x - 16y + z. In addition, find the single equilibrium solution for this system. How would you characterise the stability of this point? 5. In a previous homework question we considered a system of two springs. The homogeneous (unforced) equation for the length x = x(t) of the lowest spring was (4) + (k1 + 2k2).(2) + kikzz = 0 for when both masses mi and m2 are set to unity, and where ki and k2 are spring constants. By writing yl = X, y2 = i, y3 = i and y4 = (3), express this 4th-order differential equation as a first-order system of differential equations Hy = Ay for a matrix A which you must specify, and where y = (y1, 2, y3, y4) . What are the eigenvalues of A, and what does this tell you about the nature of the solutions? In particular, is it possible for a solution to be unbounded? Are any solutions periodic