3. (20 Points). Consider the linear system dx x + 3y dt dy =x-y dt (i) Show that the origin is the unique equilibrium point. (ii) Compute the general solution. (iii) Determine what type of equilibrium point the origin is (e.g. source, sink, etc.) (iv) Sketch the phase portrait. (v) Solve the initial value problem given by (0)=-2, y(0) = 3.