how do i find the bifurcation for this: d^x/dt^2 = -.3 x - (x - 1)/((x - 1)^2 + a^2)^(3/2) - (x + 1)/((x + 1)^2 + a^2)^(3/2) we've tried using mathematica but it just runs forever...
d/dx (x)(e^xy)(cos2x). Product rule lets me take the derivative of f(x)g(x). But three functions?
Let P(t) represent the population of a non-native species introduced to a new area for the purposes of harvesting. Suppose we intially introduce P0 = 100 indicidcuals and suppose the population grows exponentially with growth-rate coefficient k=2 if there is no harvesting (for...
Suppose a species of fish in a particular lake has a population that is modeled by the logistic population model with growth rate k, carrying capacity N, and time t measured in years. Suppose the growth-rate parameter k=.3 and the carrying capacity N=2500. Suppose P(0)=2500. (...