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sweet [91]
3 years ago
11

The following differential equation is separable as it is of the form dP/dt = g(P)h(t).

Mathematics
1 answer:
dedylja [7]3 years ago
7 0

Answer:

P(1-P) = Ae^t

Step-by-step explanation:

given differential equation is

\frac{dP}{dt} =P-P^2\\\frac{dP}{dt} = g(P) h(t)\\g(P) = P-P^2\\h(t) = 1

So this is separable

We separate as

\frac{dP}{P-P^2} =1dt\\\frac{dP}{P(1-P)} =1dt

Resolve into partial fractions to solve this

dP(\frac{1}{P}+ \frac{1}{1-P} ) = 1dt\\ln P(1-P) = t+C\\P(1-P) = Ae^t

So solution isP(1-P) = Ae^t

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