Talk:Ordinary Differential Equations/Substitution 1

Include an example of where substitution doesn't work?
Under "Other Methods", it says "Remember that between v and v' you must eliminate the y in the equation."

Maybe it would be a good idea to include an example where this doesn't work? In particular, a good example whould be where a substitution v = v(x,y) eliminates y from the right-hand-side of the DE, but it's not possible to eliminate y from the dy/dx term.

It's a common misunderstanding with, for example, integration by substitution, that if you can get rid of all of the xs from the integrand, then you should be able to solve it (they forget about the dx). A similar misunderstanding can happen with this kind of substitution, where people forget they need to eliminate the y from dy/dx.

That's why I think an example (or rather a counter-example) would be helpful. DonkeyKong64 06:42, 20 October 2007 (UTC)