Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutions!

1. Sep 1, 2011

(xy2+y2)dx + xdy = 0

the questions are:
a. Show that the equations above can be an exact differential equations!
b. Determine its solutions!

Help me please because i have working on it for 3 hours and i can't find its integration factor to change the un-exact differential equation above into an exact one. I need your help..

2. Sep 1, 2011

LCKurtz

Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

That equation isn't exact. But instead of trying to find an integrating factor, why don't you just separate the variables, which is easy?

3. Sep 2, 2011

Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

Thanks LCKurtz, but my lecturer ask me to solve it by finding its integration factor.. I wonder how it is.. Can you give me a clue?

4. Sep 2, 2011

5. Sep 2, 2011

LCKurtz

Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

I don't think so unless I was sleepy when I checked it and am still asleep. I'm guessing the problem has a typo.

6. Sep 2, 2011

micromass

Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

Hmmm, I was allso sleepy link doesn't work...

7. Sep 2, 2011

LCKurtz

Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

The link seems to work for me. It's just that the method doesn't work for this problem.

8. Sep 2, 2011

LCKurtz

Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

For what it's worth, and probably not very relevant, here's an exact DE that has the same solution set f(x,y) = C:

$$-\frac{x+1}{xy}dx + \frac{x + \ln(x) -1}{y^2}dy = 0$$

I don't see any obvious way to manipulate the original DE into this form.

To the original poster: I hope you will report back what your lecturer gives for a solution method.