5. Consider the following linear systems and their general solutions: dx dy (a) = 6x-2y, = 4x+2y dt dt with general solution x(t) 34 (1) ) = ar ( y(t) cos(2t) + sin(2t) dx dy (b) 5x+2y, = 4x+3y dt dt 4t et +2 with general solution x(t) (360) = 0) (1 ) " + (-2) 1 dx dy (c) = 3x - Y, = 6x - 4y dt dt et x(t) y(t) with general solution 1 = 1 e- = ((1)) - 9 (6) + (1) e2t dx dy (d) = -2x - Y, = x dt dt (s sin(2t) - 2 sin(2t) - cos(2t) e4t with general solution x(t) ( ) ) = ( 11 ) y(t) For each of the linear systems e-t + 2 ( -+ + 1 ) et (i) Sketch the phase portrait near the critical point at the origin. (ii) Discuss the type and stability of the critical point.