Chapter 14 page 3 - logistic diff eqn

Hi

Does anyone know how to solve the logistic differential equation half way down page 3?

The question on page 4 of the notes asks how to get from the solution for P(t) back to the differential equation but I would like to know how to solve the diff eqn:
1/P(t) . dP(t)/dt = p - kP(t)
to get P(t)

Many thanks

 

same question.

is solving this differential eqn required by subject ST4?

 

I seriously doubt you'll be asked to solve differential equations in an ST4 exam.

But if you're interested (and it's not too difficult) the top results in a google search for "solve logistic differential equation" provide the full method. In a nutshell, separate variables, integrate both sides (using partial fractions) and simplify.