Given the following system of linear differential equations:
x'1 = -3x1+ 2x2
x'2 = -3x1+ 4x2
i) Determine the general solution of system.
ii) Compute the solution of the system satisfying initial conditions: x1(0) = 2, x2(0) = -1.
iii) Compute all a1 and a2 such that if x(t) = (x1(t) , X2(t)) [matrix] is solution of system with initial condition x(0) = (a1, a2) [Matrix] then x(t) goes to 0 as t approaches inifinity.
iv) Same as part iii (but with Beta) as t approaches negative infinity.