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Homework Help: Integrated Factors (DE)

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data

    I have been dealing with Exact Equations in my DE class, and I came around this problem.


    This is obviously not an exact eqn. So I tried using integrated factors on it and try to find this "factor" μ.
    But no matter if I did it in terms of t or in terms of y, I couldn't separate it in terms of one variable.




    2. Relevant equations

    Is there any way that you can find an integrated factor which it is in terms of both variables?
    instead of t or y alone, both?

    3. The attempt at a solution

    I tried everything, and this topic is not even covered in class or in the book. I learnt this on my own and I have only learn Integrated factors in terms of y or in terms of t, not both.

    Help please.
  2. jcsd
  3. Feb 4, 2012 #2


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    A function ##M(x,y)## is said to be homogeneous of order n if ##M(\lambda x,\lambda y)= \lambda^nM(x,y)##. If ##M(x,y)## and ##N(x,y)## are both homogeneous of degree n, then the differential equation ##M(x,y)dx + N(x,y)dy = 0## can be converted to a separable DE with the substitution ##y=ux##.

    That applies to your question. Look at http://www.cliffsnotes.com/study_guide/First-Order-Homogeneous-Equations.topicArticleId-19736,articleId-19713.html [Broken] for a discussion of this type of equation.
    Last edited by a moderator: May 5, 2017
  4. Feb 5, 2012 #3
    Thanks, that just lighted a bulb in my head.
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