solve all the parts please

3. There are two species of fish live in a pond that compete with each other for food and space. Let x and y be the populations of fish species A and species B, respectively, at time t. The competition is modelled by the equations dx = x(a - b,x - cy) dy dt -= y(a2 - bzy = (2x) where di. by, Ci, a2, b2 and c2 are positive constants. (a). Predict the conditions of the equilibrium populations if (1). bib2 C, C2 (2 marks) (b). Let a, = 18, a2 = 14, b, = by = 2, c, = c2 = 1, determine all the critical points. Consequently, perform the linearization and then analyze the type of the critical points and its stability. (13 marks) (c). Assume that fish species B become extinct, by taking y(t) = 0, the competition model left only single first-order autonomous equation = x(a, - b,x) = f(t,x) Let say a, = 2, b, = 1, and the initial condition is x(0) = 10. Approximate the x population when t = 0.1 by solving the above autonomous equation using fourth-order Runge-Kutta method with step size h = 0.1