Solution of the Logistic Equation 6

Logistic equation formula. The virtue of having a single, first-order equation representing yeast dynamics is that we can solve this equation using integration techniques from calculus. First we separate variables in (3), annd then we apply partial fractions to the left-hand-side: Now we can integrate both sides directly, using the facts that. Putting these three integrals together, relabelling constants , and using gives. or, exponentiating both sides, where . Note that when we can see that. Now we can solve for , This is the general form of the solution to the logistic equation, (3). If we want to see explicitly how the initial conditions for the yeast population figure in we can substitute and to get. The behavior of typical solutions is plotted in Figure 1.