Talk:Inseparable differential equation

Rated article

I rated this article as a stub because it doesn't cite anything and might have original research (violating WP:NOR). As for importance, I rated it as Mid-importance, which is lower than the similar articles Ordinary differential equation, Partial differential equation (both Top) but same as Separable differential equation (rated Mid). Please review it; thanks. Duckmather (talk) 20:31, 26 April 2021 (UTC)

What proportion of IFOLDEs yield to the integrating factor method?

The article reads: "This can be used to solve almost all inseparable equations containing no y to a degree other than one, i.e., linear differential equations."

What does "almost all" mean here? I'm not a professional mathematician, but it seems likely to me that the set of inseparable 1st order linear differential equations is infinite, so what we mean by "all of them" is unclear and in turn "almost all" is unclear too.

If we take a given IFOLDE that is soluble by this method, it seem to me that we could generate another insoluble IFOLDE by modifying q(x) by multiplying it by some function that renders

$\int \mu \,q(x)\,dx$

impossible to do. As there is any number of ways of modifying q(x) to this it seems for every IFOLDE that is soluble by this method, we can generate any number of IFOLDEs that aren't. In which case, the method only works for a tiny fraction of IFOLDEs.

Now that's an extreme argument, and maybe a mathematician could demolish it. But being more down-to-earth, if you said "most of the IFOLDEs that you come across can be solved by using this method", the truth of that statement would depend upon the nature of the IFOLDEs that you come across.

I think it would be better to say something deliberately vaguer but defensible such as "many simple IFOLDEs can be solved using this method".

Macboff (talk) 12:30, 24 April 2022 (UTC)

Now this is a redirect

I decided to make this a redirect to Ordinary differential equation since almost every ODE isn't separable. Duckmather (talk) 14:47, 16 June 2022 (UTC)