I'm looking for some proofs about the following statement:

let be a homogeneous ODE.

find an integrating factor for the above equation.

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- Oct 1st 2010, 09:31 PMKrizalidHomogeneous equations always do have an integrating factor
I'm looking for some proofs about the following statement:

let be a homogeneous ODE.

find an integrating factor for the above equation. - Oct 2nd 2010, 06:29 AMJester
If the ODE is homogeneous then it admits the symmetry

or infinitesimal transformation

and the original ODE has the integrating factor

(we can set wlog)

This was show by Lie in the late 1800's. - Oct 3rd 2010, 05:38 AMHallsofIvy
Let me point out that "find an integrating factor" is NOT a statement and you are not trying to prove it.

In fact,**any**first order differential equation has an integrating factor- its just simpler to find if the equation is homogeneous. - Oct 3rd 2010, 08:11 AMKrizalid