A population biologist tells us that the rabbit and wolf populations in his region
dr/dt=5r−w, dw/dt =3r+w
(In the absence of wolves, the rabbit population would grow exponentially: dr/dt = 5r; but wolves eat rabbits and slow down the growth. In the absence of rabbits, the wolf population would grow exponentially: dw/dt = w; but wolves do better when there’s more to eat, so the presence of rabbits increases the growth rate.)
(a) Find the general solution.
(b) If r(0) = w(0) = 10, what are the populations at time t?
(c) After a long time, what will be the ratio of rabbits to wolves?
(d) Is this a plausible model?