Question

How do i solve a differential equations problem that involves the logistic model equation but the equation is not in the default form?

Answer 1

for instance, instead is not the normal one:
\[\frac{ dP }{ dt } = kP(1-\frac{P}{K})\]
but slightly different:
\[\frac{ dP }{ dt } = kP(7-\frac{P}{K})\]

Answer 2

are the k and K constant?

Answer 3

?

Answer 4

\[\frac {dP}{P(7 - \frac{P}{k})} = kdt\]

Answer 5

now solve

Answer 6

\[\frac{-dP}{7P} + \frac{dP}{7K(\frac{P}{K} - 7)} = -kdt\]