1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Variable Separation

  1. Aug 28, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]x^2y'=1-x^2+y^2-x^2y^2[/tex]

    2. Relevant equations

    n/a

    3. The attempt at a solution

    I am trying to separate the y terms on one side and the x terms on the other so I can solve this differential equation. I've tried everything I can think of, but cannot get them on their respective sides.

    Any hints starting in the right direction?
     
  2. jcsd
  3. Aug 28, 2010 #2
    [tex]x^2y'=(1-x^2)+(1-x^2)y^2[/tex]
     
  4. Aug 28, 2010 #3
    That was actually what I tried in the beginning.

    Next I tried dividing everything by x^2 to get y' alone. Then tried subtracting (1-x^2)y^2. Then spent the next ten minutes moving things back and forth until I started over.

    This is really stupid, but say I am dividing both sides by y^2. It has to go into all three pieces, correct? It doesn't just get cancelled out one the one side, does it?
     
  5. Aug 28, 2010 #4
    hmm, you can factorize [tex]
    (1-x^2)
    [/tex]

    [tex]
    (1-x^2)(1+y^2)
    [/tex]

    ;P
     
  6. Aug 28, 2010 #5
    Haha, thanks.

    I love spending forever on some problems, only to find out the easiest method is the correct answer. I always get stuck on the easiest ones. I don't get it. :rofl:


    [tex](1-x^2)(1+y^2) = 1-x^2+y^2-x^2y^2[/tex] aka the original problem. I don't think they make factoring problems easier than that.:tongue:
     
    Last edited: Aug 28, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook