Differental Equation homework (w/ calc 2 intergrals)

  • Thread starter mandymandy
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  • #1

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


Homework Equations


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)


Please help! Thanks. :)
 

Answers and Replies

  • #2
LCKurtz
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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


Homework Equations


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)


Please help! Thanks. :)
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.
 
  • #3
I can solve it from here I don't know why I was so confused. :) thanks
 

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