Find the most general real-valued solution to the linear system of differential equations I' [2-25] = X x(t) y(t) help (formulas) -8-8== In the phase plane, this system is best described as a source/unstable node O sink / stable node saddle center point / ellipses spiral source spiral sink none of these help (matrices)

Find the most general real-valued solution to the linear system of differential equations [1 -2] a. 5 x1(t) -e^(3t) = ci + c2 x2(t) e^(3t)

The system of differential equations has a general solution where x₂ (t) = = = x₁ (t) Im (ea) Im (e^¹¹b) Im (e^tc) 3 9 -9 = 0 1 2 4 -1 -1 x(t) = C₁x₁ (t) + C2x2 (1)+c3x3 (t) X Re (e^₁¹ a) Re (e^₁¹b) Re (e^¹¹ c)

Can you find all equilibria of each system of differential equations and use the analytical approach to determine the stability of each equilibrium? dx1/dt= 4x1(1-x1)-2x1x2 dx2/dt= x2(2-x2)-x2