# simple autonomous ODEWatch

#1

am i right in thinking this is not homogeneous, since the 1 is there

am i right in thinking this is autonomous since the dependent variable does not appear??*

*since this can be written making it non autonomous but i dont think it matters otherwise could be written i just want to clarify
0
8 years ago
#2
(Original post by Chaoslord)

am i right in thinking this is not homogeneous, since the 1 is there
Yes it is not homogeneous as the RHS would = 0 if it was.

(Original post by Chaoslord)
am i right in thinking this is autonomous since the dependent variable does not appear??
You are right in saying it is autonomous but your reason is wrong. It is autonomous because the independent variable does not appear.
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#3
(Original post by TheEd)
Yes it is not homogeneous as the RHS would = 0 if it was.

You are right in saying it is autonomous but your reason is wrong. It is autonomous because the independent variable does not appear.

sweet, that was just a typo xD my ts in my example should have made that clear =P but yea thanks
0
8 years ago
#4
(Original post by Chaoslord)

am i right in thinking this is not homogeneous, since the 1 is there

am i right in thinking this is autonomous since the dependent variable does not appear??*

*since this can be written making it non autonomous but i dont think it matters otherwise could be written i just want to clarify
dx = dt
integration of dx = integration of dt
Therefore x = t + c.

EDIT: And uh yes it is autonomous because t does not appear on the RHS.
0
8 years ago
#5
(Original post by Chaoslord)

am i right in thinking this is not homogeneous, since the 1 is there

am i right in thinking this is autonomous since the dependent variable does not appear??*
Note that there is more than one meaning for "homogeneous differential equation".
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#6
(Original post by DFranklin)
Note that there is more than one meaning for "homogeneous differential equation".

edit: scratch that, just googled - cheers (though i dont think i'll need to know all that for the course i'm doing)
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#7
(Original post by RBarack)
dx = dt
integration of dx = integration of dt
Therefore x = t + c.

EDIT: And uh yes it is autonomous because t does not appear on the RHS.
um, cheers but integrating that wasn't the issue... i made that equation up just to clarify my understanding of autonomous and homogeneous, sorry
0
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