# Differental Equation homework (w/ calc 2 intergrals)

## Homework Statement

Carrying capacity N of a population

Assume: small population, dp/dt is proportional to P

if 0<P<N then p(t) increases
if P>N then P(t) decreases
equilibrium means dp/dt = 0

dP/dT = KP(N-P)

Solve for P(t)

## The Attempt at a Solution

∫dP/P(N-P) = ∫kdt ?

My teacher said we'd be using ln(...) and 1/[P(N-P)] = A/P + B/(N-P)

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## Homework Statement

Carrying capacity N of a population

Assume: small population, dp/dt is proportional to P

if 0<P<N then p(t) increases
if P>N then P(t) decreases
equilibrium means dp/dt = 0

dP/dT = KP(N-P)

Solve for P(t)

## The Attempt at a Solution

∫dP/P(N-P) = ∫kdt ?

My teacher said we'd be using ln(...) and 1/[P(N-P)] = A/P + B/(N-P)

You are on the right track. Perhaps you need to review partial fractions to work the integral$$\int \frac{1}{P(N-P)}\, dP$$Your teacher gave you a pretty good hint there.