Solving ODE: (xy^2 + y^2)dx + xdy = 0 - Exact Solutions

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Homework Help Overview

The discussion revolves around the problem of determining whether the given differential equation, (xy² + y²)dx + xdy = 0, is exact and finding its solutions. The subject area is ordinary differential equations (ODEs), specifically focusing on exact equations and integrating factors.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the nature of the differential equation, with some suggesting that it is not exact and proposing alternative methods like separation of variables. Others emphasize the requirement to find an integrating factor as per the lecturer's instructions.

Discussion Status

The discussion is ongoing, with participants sharing differing views on the approach to take. Some guidance has been offered regarding resources for finding an integrating factor, although there is uncertainty about the applicability of these methods to the original problem. Multiple interpretations of the problem's requirements are being explored.

Contextual Notes

There is mention of a potential typo in the problem statement, and some participants express confusion regarding the provided resources for finding an integrating factor. The original poster is under the constraint of needing to follow specific instructions from their lecturer.

adrianwirawan
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(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:
 
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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?
 


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?
 


micromass said:
The following site gives you some information on how to determine an integration factor; http://www.sosmath.com/diffeq/first/intfactor/intfactor.html

Case 2 is of interest here...

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.
 


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


micromass said:
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.
 


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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