1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?