Final answer:
To determine the equilibrium points of the provided system of differential equations, one must set the derivatives equal to zero and solve for x and y, leading to a set of simultaneous equations that yield the equilibrium points. The correct option is b) Determine the equilibrium points of the system.
Step-by-step explanation:
The question is asking to determine the equilibrium points of the system of differential equations given by dx/dt = 2x(y - x) and dy/dt = (4 - x)yx. To find the equilibrium points, we set dx/dt = 0 and dy/dt = 0 and solve for x and y.
For dx/dt = 0, either x = 0 or y = x. For dy/dt = 0, we must have y = 0 or x = 4. The equilibrium points can then be found by solving the resulting simultaneous equations.
The specific solution to these equations was not provided, but the approach described allows us to find the equilibrium points, which are key to understanding the behavior of the system.
The given system of differential equations is a set of ordinary differential equations. To complete the question, the best statement would be:
b) Determine the equilibrium points of the system.
To determine the equilibrium points, we need to set both equations equal to zero and solve for x and y. By finding the values of x and y that satisfy both equations, we can determine the equilibrium points of the system.
The correct option is b) Determine the equilibrium points of the system.