# Ok, so now how do you separate this one?

1. Dec 10, 2006

### prace

$$\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8}$$

I want to solve this DE using the separation technique. Any ideas on how to start?

And just for myself, and maybe anyone else. Is there a sort of systematic approach to finding out how to start these problems? It seems like I will work a few no problem, then get to one and just stare for awhile. Maybe if there was some sort of method to the madness, then it might make things easier. Just a thought.

Thanks!

2. Dec 10, 2006

### AKG

Factor.........

3. Dec 10, 2006

### prace

umm... Sorry if this sounds lame, but I don't see what I am to factor here.

4. Dec 11, 2006

### AKG

the numerator and denominator.

5. Dec 11, 2006

### prace

Could you please be a little more specific? Do you mean just divide the two using long division? Hmmm... ok, I will try that and see if I can get to something. Thanks.

6. Dec 11, 2006

### prace

ok, so I tried it and I got $$1+\frac{5(x-y+1)}{xy-2x+4y-8}$$ which does not seem to help me out too much.

The form of both the numerator and the denominator do look a little suspicious. Is there a way to factor them like we can for a problem in the form $$ax^2 + bx + c$$?

7. Dec 11, 2006

### dextercioby

He said "factor" meaning $xy-3+3x-y=(x-1)(y+3)$.

Is that a better hint ?

Daniel.

8. Dec 11, 2006

### AKG

Factor the numerator and factor the denominator. Isn't that exactly what I said?

9. Dec 11, 2006

### prace

Yes you did AKG, sorry about that. I just did not see how to factor them. I guess I am not very strong with my factoring and it was not very clear to me.

Thanks for the hint Daniel, that will help me out a lot.

Ok, going to go and work this out now!