System of DEs: Linear or Nonlinear? Competitive or Cooperative?

[mathlete]

$$\frac{dx}{dt} = -5x+2xy$$
$$\frac{dy}{dt} = -4y+3xy$$

Are these linear or nonlinear? I'm inclined to say non-linear but using maple it tells me it's linear ( odeadvisor(ode1, [linear]); returns [_linear] where ode1 is dx/dt).

Also, are they competitive or cooperative? I know it's not predator prey. I've graphed it and all solutions tend to 0, but I don't know what type that is (I can't find an explanation of cooperative/competitive anywhere on the internet)

 

[mathman]

For the first question, they are definitely non-linear (xy terms). Maple is just wrong.

I can't answer the second question.

 

[Tide]

Apparently, you asked Maple whether the first equation is linear - which it is. With respect to the first equation alone, y = y(t) and it's clearly linear in the dependent variable x. The real question is whether the system of equations is linear - which it is not since the equations involve a product of the variables x and y.

For the second question you will have to resort to reading your textbook to know what the authors mean by cooperative vs. competitive.

 

[mathlete]

OK thanks, I thought it had something to do with me just asking it about the one equation instead of the system.