Re: Help with solutions to two DEs


Ο <carlos5100@xxxxxxxxx> έγραψε στο μήνυμα
news:1119647583.173194.318430@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> Ok, thanks for the information on the first DE. I see what you mean how
> only for a certain range of C it is a solution to the DE, I did not
> even think about that aspect of it. However, this brings up another
> question, what is the correct way to write that solution? do you just
> normally write it as a piecewise function or do you normally just write
> off to the side for a certain interval of C this given solution is
> correct?
>
> *slaps his forehead* oops, I just completely looked over how to solve
> for the second DE, thanks for that hint.
>
> I end up getting the below for the Second DE
>
> y=(1-Ce^(-e^x))/4
>
> which i guess means this solution is valid for -inf<x<inf

Be careful. The solution of

ln(|y-4|/|y|)=-e^x+C, is

y=-4/(exp(-exp(x)+C)-1)

(NOT y=(1-Ce^(-e^x))/4)

and there is one more solution if you alow complex values for C:

y=4/(exp(-exp(x)+C)+1)

The denominator(s) must never be zero. What can you conclude from the above?

> Thanks for the help.
>
> Sam J.
--
I. N. Galidakis
http://users.forthnet.gr/ath/jgal/
Eventually, _everything_ is understandable

.

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