proving DE not separable (partials technique???)

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Posted by Colin on September 11, 2002 at 11:18:06:

A while back (see 8/8 posting) Subhotosh made a statement about a partials technique used to prove the unseparability of a DE. Can anyone explain this?

I have a problem:
dy/dx = (y - 4x)/(x - y)

I need to prove it is not separable. How can I do it formally? It is pretty clear if I try it, but I don't know if that is a sufficient "proof" to show a couple failed attempts...

Colin

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