volterra obtained differential equations of the forms dx/dt=x(a1+a2y) dy/dt=y(b1
ID: 2967740 • Letter: V
Question
volterra obtained differential equations of the forms dx/dt=x(a1+a2y) dy/dt=y(b1+b2x) as a mathematical model describing the competition between two species coexisting in a given environment. from this sistem one obtains (by the chain rule, in other words, dy/dx = dy/dt*dt/dx) the separable differential equation dy/dx=(y(b1+b2x)/x(a1+a2y)). solve this differential equation.
assume that a population grows according to verhurst's logistic law of population growth. dN/dt=AN-BN^2 where N =N(t) is the population at time t, and the constatns A and B are vital coefficients of the population. what will the size of this population be at any time t? what will the population be after a very long time, that is, as t approaches infinity?
solve both with all work.
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