Are integrating factors still an active field of research? (are there equations for which it's still an open question whether integrating factors exist?)

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- Sep 7th 2010, 04:03 PMwonderboy1953Integrating factors question
Are integrating factors still an active field of research? (are there equations for which it's still an open question whether integrating factors exist?)

- Sep 8th 2010, 04:43 AMJester
I don't know if it's an "active" area of research but to your second question, yes there are ODEs which, in general, don't have know integrating factors. Here's a particular equation

$\displaystyle \dfrac{dy}{dx} = \dfrac{x+y}{xy},$

- an Abel equation of the second kind. Or, in general

$\displaystyle y \dfrac{dy}{dx} = a(x) y + b(x)$.