Hi,

I don't think I know how to do all of this yet however:

The evolution of a population of rhinoceros, R(t), in hundreds, time in years, in anAfrican National Park is given by the equation,

dR/dt =1/5R(2 − R); R(0) = 0.5

(a) Solve the system exactly for R(t).

(b) What happens as the time t → ∞, i.e. what is the population a long time in the future?

(c) Write an Euler scheme and compute until the population levels off (using Excel, Matlab,Octave, LibreCalc or similar).

(d) Plot both of your solutions on the same set of axes and comment.

(a) dR/dt = 1/5 R(2-R)

Multiply R through brackets -dR/dt = 1/5 2R + R2 or dR/dt = 2R+R^{2}/5

Divide both sides by dR -dt = (2R+R^{2)}/5

If I am correct I can see dt = a number plus its derivative - does this mean I can use integration by substitution setting R^{2 }as the number to be substituted? Or am I on the complete wrong planet?

Also for(b) am I looking for the absolute maxima of the equation?

Kind regards

Beetle