I am having problems with solving systems of differential equations. x'= [(-3 ) (gamma)]x .....[ ( 6 ) ( 4 ) ] I am supposed tofind the interval of values of gamma for a) stable focus and b) stable node. I started by [(-3-r) (gamma)][x1] =  [( 6 ) (4-r ) ][x2].... det(A-rI) = (-3-r)(4-r)-6(gamma) = 0 = r^2-r-12-6(gamma)= 0 but I don't know where to go after this point to find these different intervals. For another problem: x'= [0 3]x .....[-12 0] with initial conditions x1(0)= 1, x2(0) = 2 show that the solution x(t) is periodic and determine its period. Additionally to find the moment(s) when the point x(t) is closest to the equilibrium point 0. For this I have [(-r ) (3)][x1] =  [(-12) ( -r)][x2].... so r^2 + 36 = 0 how do I or do I factor this? and after I find my values of r and plug them back in, where do I go?