# A Differential Equation

1. Jun 2, 2005

This is out of a P3 (OCR) text book so it should be dead easy but I just can't see the answer. I know it is not a simple ln(N(500-N)) because the differential is not on top. Anyway here it is:

(5000)dN/dt=N(500-N)

they also say when N = 100, dN/dt = 8 (which is obvious)

the answer in the back of the book is:

t=(10)ln(N/(500-N))+k

Cheers

Last edited: Jun 2, 2005
2. Jun 2, 2005

### Nylex

Hmm, most people here won't know about the exam boards we have . Have you done anything on the question and if so, could you post it?

Edit: what did you mean by the differential's not on top?

I'm stuck trying to integrate $$\int \frac{dN}{N(500 - N)}$$. Argh :/.

Last edited: Jun 2, 2005
3. Jun 2, 2005

The numerator

This is a variable seperable right?

so you take the N(500-N) to the left side, split the dN and the dt to get:

int[ 1/{N(500-N)} ] dN = int[ 1/5000 ] dt

Now by chain rule (I think), if the differential is on the top of the fraction you can just say it is the log of the denominator. eg int [1/x] dx = ln|x|+c

However, the differential is not on the top in this case so I am screwed.

4. Jun 2, 2005

### shmoe

Partial fractions will work.

5. Jun 2, 2005

oh yeah sometimes you can be so obsessed looking for something really complicated and miss something simple. It does work. Thanx

6. Jun 2, 2005

### inha

break the numerator into 2 pieces. I don't remember how you say that in ze english, partial fraction decomposition or something.

7. Jun 2, 2005