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Math Help - Integrating factors question

  1. #1
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    Integrating 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?)
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  2. #2
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    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

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

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

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