Question

What makes a differential equation autonomous or homogeneous? Could you please give me an example with numbers instead of a proof?

Answer 1

a homogeneous DE has can be set =0 with all y-terms on the other side
examples:
y''-3y'+y=0
(y')^2-y=0

non-homogeneous:

y''-3y'+y=x
y'-7y=12
y'-7y+x=0

notice the last is not homogeneous because all the y's being put on one side gives
y'-7y=-x

not sure about the autonomous thing....

Answer 2

I think autonomous is the same as non-homogenous, I think

Answer 3

I kinda wanted to assume that, but wikipedia confused me
http://en.wikipedia.org/wiki/Autonomous_system_(mathematics)

Answer 4

This kind of explains the autonomous thing if ya'll need it for your class: http://livetoad.org/Courses/Documents/214a/Notes/autonomous.pdf

From what I understand, autonomous and non-homogenous aren't the same things. According to the link, an autonomous equation is one where y' depends on y instead of t, which would be the independent variable in y. Does this sound right?

Answer 5

And thank you both for helping me.