Homework Help: Variable Separation

1. Aug 28, 2010

erok81

1. The problem statement, all variables and given/known data

$$x^2y'=1-x^2+y^2-x^2y^2$$

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. Aug 28, 2010

annoymage

$$x^2y'=(1-x^2)+(1-x^2)y^2$$

3. Aug 28, 2010

erok81

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?

4. Aug 28, 2010

annoymage

hmm, you can factorize $$(1-x^2)$$

$$(1-x^2)(1+y^2)$$

;P

5. Aug 28, 2010

erok81

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:

$$(1-x^2)(1+y^2) = 1-x^2+y^2-x^2y^2$$ aka the original problem. I don't think they make factoring problems easier than that.:tongue:

Last edited: Aug 28, 2010