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

1. Sep 24, 2011

### tempneff

[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. Sep 25, 2011

### HallsofIvy

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).