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Homework Help: Ok, so now how do you separate this one?

  1. Dec 10, 2006 #1
    [tex]\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8}[/tex]

    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. jcsd
  3. Dec 10, 2006 #2

    AKG

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    Factor.........
     
  4. Dec 10, 2006 #3
    umm... Sorry if this sounds lame, but I don't see what I am to factor here.
     
  5. Dec 11, 2006 #4

    AKG

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    the numerator and denominator.
     
  6. Dec 11, 2006 #5
    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.
     
  7. Dec 11, 2006 #6
    ok, so I tried it and I got [tex]1+\frac{5(x-y+1)}{xy-2x+4y-8}[/tex] 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 [tex]ax^2 + bx + c[/tex]?
     
  8. Dec 11, 2006 #7

    dextercioby

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    He said "factor" meaning [itex] xy-3+3x-y=(x-1)(y+3) [/itex].

    Is that a better hint ?

    Daniel.
     
  9. Dec 11, 2006 #8

    AKG

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    Factor the numerator and factor the denominator. Isn't that exactly what I said?
     
  10. Dec 11, 2006 #9
    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!
     
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