# Differential Equation

• Sep 1st 2008, 09:33 AM
Differential Equation
Just revising for my next year courses and going over last years stuff and need to brush up a bit on what should be a simple problem...

Q) Find the solutions of the following equations of population biology

$\displaystyle \frac{dN}{dt} = k(M - N)$, $\displaystyle N(0) = N_0$

Where k and M are positive constants.

This really should be easy but after exams I always get a memory block until the courses restart...

Where I've got up to...

$\displaystyle \lambda + k = 0$, $\displaystyle \lambda = -k$

so general solution is $\displaystyle (M - N)e^{-kt}$ or something like that... Then you do something like have a particular solution which is just kM... possibly..?
• Sep 1st 2008, 10:33 AM
Jhevon
Quote:

Just revising for my next year courses and going over last years stuff and need to brush up a bit on what should be a simple problem...

Q) Find the solutions of the following equations of population biology

$\displaystyle \frac{dN}{dt} = k(M - N)$, $\displaystyle N(0) = N_0$

Where k and M are positive constants.

This really should be easy but after exams I always get a memory block until the courses restart...

Where I've got up to...

$\displaystyle \lambda + k = 0$, $\displaystyle \lambda = -k$

so general solution is $\displaystyle (M - N)e^{-kt}$ or something like that... Then you do something like have a particular solution which is just kM... possibly..?

see post #2 (and #8, if you want) here. a similar example is worked out