Re: Help with a differential equation

In article <a5Vae.11616$V02.11418@xxxxxxxx>,
Ron Sperber <ronsperber@xxxxxxxxxxxxx> wrote:

> A N Niel wrote:
> > In article <kjSae.11446$V02.5881@xxxxxxxx>, Ron Sperber
> > <ronsperber@xxxxxxxxxxxxx> wrote:
> >
> >
> >>I don't know about your textbook, but most of the introductory DE
> >>textbooks I've seen only deal with linear first order ODEs which this
> >>definitely is not.
> >>
> >>However the following trick might be useful
> >>
> >>Let u=(y/x).
> >
> >
> > Look under "homogeneous" in your textbook, and you will find that trick.
> > But we don't call it a trick, we call it a method.
>
> Ah, I think now I know the confusion I had. Sadly homogeneous in ODEs
> refers to both these types of equations and ODEs of the form
> F(x,y,y')=0. And while I've seen these in some books, its sometimes
> relegated to exercises and I don't always teach this "method".
> And frankly your comment of "we call it a method" is just silly. Many
> 'methods' of solving ODEs ARE tricks. They're just tricks that work.

The standard definition of a method is a trick that works
more than once.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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