# Math Help - Integrating factors question

1. ## 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?)

2. 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

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