Please answer the following conceptual questions. Please justify your answers by short arguments. (1) Consider for a matrix A € Mat(2; R), an initial value uo € R2 and an unknown function u: u:R → R2 the IVP ſu(t)= Auſt), (u(0) = . Consider for 1 1. Provide necessary and sufficient conditions on the polynomial p, such that the solution of the IVP with initial value 2(0) = 1o exist for all t E (0,0) and stays bounded for any choice of initial value to ER. (3) Consider for an unknown function u :ICR + R2, u(t) = (z(t), y(t)), the system of the form f(t) = f (x(t), (t), y(t) = fz((t), y(t)), where f1, f2 : Rx R+R are polynomials in two variables (e. g fi(r, y) = ry2 + x). Please provide an example for fi and f2, such that the resulting ODE has exactly three distinct equilibrium points and moreover one of them is stable and two of them are unstable.