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From: Blue Venom on 5 May 2010 05:54
05/05/2010 9.59, Alois Steindl:

> Hello,
> since that sounds much like a homework, you should definitivly try to do
> it yourself. If you don't have any clue, you should read, what you have
> learned in the recent lectures; if you don't understand that, you have
> to go back, until you understand it.
> Newsgroups are not for cheating.
> Alois

Hello, this is homework of a course I did not and will not attend, so
nobody is grading these things (not even taking a look at them in
facts). I'm doing this because I'm attending another course about ODEs
and there are prerequisites I do not know. The exercises usually (this
one for instance) have many more questions (that I answer by myself). I
just post what I cannot get to grips with in a reasonable amount of time.

Bye bye

From: Blue Venom on 5 May 2010 05:56

> Hint:
>
> sinh(x) satisfies the differential equation
> y' = sqrt(1+y^2).
>
> Best wishes
> Torsten.

Thanks, It was what I first thought about, although the calculations
were clearly wrong as it didn't look true to me the first time (it does
now).
From: Ray Vickson on 5 May 2010 12:24
On May 5, 2:56 am, Blue Venom <mandalayray1...(a)gmail.com> wrote:
> > Hint:
>
> > sinh(x) satisfies the differential equation
> > y' = sqrt(1+y^2).
>
> > Best wishes
> > Torsten.
>
> Thanks, It was what I first thought about, although the calculations
> were clearly wrong as it didn't look true to me the first time (it does
> now).

What does this sentence mean? It is unclear what you are claiming and
what you believe to be the case now.

R.G. Vickson
From: Blue Venom on 5 May 2010 12:38

> What does this sentence mean? It is unclear what you are claiming and
> what you believe to be the case now.

That the hint helped me. I'd already thought about it (before posting)
but when I calculated sqrt(1+senh(x)^2) I made a stupid mistake and
things didn't add up.
From: Ray Vickson on 5 May 2010 13:04
On May 4, 6:00 pm, Blue Venom <mandalayray1...(a)gmail.com> wrote:
> y'=SQRT(1+x2+y2)
> y(0)=0
>
> Assuming there exists a local and unique solution defined on (-d,d),
> prove that the solution y is defined for all x in R and that y(x) >=
> sinh(x) for all x >=0.
>
> Any hint?

Sorry, I take back what I said in my first reply. I used the wrong DE
(forgot the "1+" on the right). When I re-solve using the *correct* DE
numerically I DO get your original conclusion; that is, it does appear
that y(x) >= sinh(x) for x >= 0 with the inequality being strict (and
growing) for x > 0. I should learn not to post messages when I am
tired.

However, as far as a proof goes, I have no helpful hints to offer.

R.G. Vickson
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