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Can someone name this method testing DE's to be homogeneous

  1. Sep 24, 2011 #1
    [PLAIN]http://www.tempneff.com/jailtime/differential%20equations/HDE.PNG [Broken]

    I learned how to solve homogeneous DE's from youtube videos. This presented a problem when during my last test, a question stated that i should show a DE to be homogeneous. The way I learned was different then the rest of the class and I missed the points. But it works. I want to find some documentation so that I may challenge my professors grading. But....I don't have anything other than these videos.

    http://www.wikihow.com/Solve-Differential-Equations


    Specifically, i want to identify the test used in these videos that changes the DE to terms of F(x\y).
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 25, 2011 #2

    HallsofIvy

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    The usual definition of "homogeneous" (for first order equations) dy/dx= f(x,y) is that we must have f(ax, ay)= f(x, y)- that is any number multiplied by both x and y cancels.
    If we define u= y/x, we have y= xu so f(x, y)= f(x, ux) and now we can think of x as the number multiplying 1 and u: f(x, y)= f(x, ux)= f(1, u). And since "1" is a constant, we can say f(x, y)= f(1, u)= F(u)= F(y/x) where "F(u)" is defined as f(1, u).
     
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