Re: Not many solutions to this differential equation?

renardym@xxxxxxx wrote:

There are many more solutions to this problem. Consider t as
a function of f rather than the other way. Then your condition is
t'(4f/5)=5t'(f). The general solution of this is
t'(f)=f^a q(ln f),
where
a=ln 5/(ln 4-ln 5),
and
q is a periodic function with period ln(4/5).


Interesting. For a minute I thought you meant "t(f) = ..."
rather than "t'(f) = ...". You'd have to choose the periodic
function in such a way that t remains a one-to-one function
of f (since I was interested in f as a function of t rather
than vice-versa.

Finding that a proposition is false is always a good excuse
for failing to find a proof that it's true.

Thank you. -- Mike Hardy


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