# Differential equation - population of a city

• November 13th 2010, 04:18 AM
jenkki
Differential equation - population of a city
A model for the population of a city is given by:

$\frac{dp}{dt} = -4*10^{-8}p^2 + 0,56p -16*10^5$

$p(0) = 6*10^6$

And then I should find an expression for the population, p(t) (after t years). But how do I begin? The right side can also be written like: $-4*10^{-8}(p-10^7)(p-4*10^6)$
• November 13th 2010, 04:27 AM
Ackbeet
The equation is separable.
• November 13th 2010, 04:43 AM
jenkki
Quote:

Originally Posted by Ackbeet
The equation is separable.

like:

$-\frac{1}{4*10^{-8}}\int\frac{1}{(p-10^7)(p-4*10^6)} dp = \int 1 dt$ ?
• November 13th 2010, 06:16 PM
Ackbeet
Looks good so far! I'd use partial fractions on the LHS.