The solution should be original and not someone else's work. Please show all steps in detail.

Consider the system of equations x' (t) = -13(t) - 2x2(t)y(t), y' (t) = 2y3 (t) + 12 ( t )y(t). (a) Find a choice of parameters a, b, c such that the function r(t) = ax(t) +br(t)y(t) +cy?(t) satisfies the inequalities r(t) 20, r'(t) 20. (b) Make a conclusion about the stability of the equilibrium point r = 0, y = 0