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