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

  • #1
(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..

:cry:
 

Answers and Replies

  • #2
LCKurtz
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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


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?
 
  • #6
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Hmmm, I was allso sleepy :blushing: link doesn't work...
 
  • #7
LCKurtz
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Hmmm, I was allso sleepy :blushing: link doesn't work...
The link seems to work for me. It's just that the method doesn't work for this problem.
 
  • #8
LCKurtz
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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:

[tex]-\frac{x+1}{xy}dx + \frac{x + \ln(x) -1}{y^2}dy = 0[/tex]

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.
 

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