The term 'homogeneous' has two meanings in ODEs: linear equations with no forcing term, and equations of the form y' = f(y/x).
The first one is the only one that should be used. The second one makes me angry every time I see it.
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Drastic times call for drastic measures...
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Somethings just don’t need to be given their own name. e.g. the “Lorenz” force
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Wait, how did the second type of equation ever get to be called “homogeneous”? The first usage has been well-established for a looong time, IIUC
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It's a generic English word. We're lucky it only has two meanings. Compare that to something like "normal". I'm actually unclear what is "homogeneous" about the first type. Each term homogeneously depends on the independent variable?
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Yes, only the first one should be called homogeneous
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Nice! A homogeneous ODE: D^2y+m^2y=0 (y=Acos(mx)+B sin(mx), D:=d/dx) and f(x,y)=x^2+xy+y^2 with: f(tx,ty)=t^2f(x,y) is a homogeneous function of order 2.
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Angry
...that’s a very strong emotionThanks. Twitter will use this to make your timeline better. UndoUndo
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As much as I agree that homogeneity in the first sense is more familiar, one has to wonder how useful it is in describing the equation/dynamics in a useful way? Homogeneity is also a property of functions or equations and just so happens to apply to ODE
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