When I was younger, a teacher of mine gave me

this problem for training:

http://perso.wanadoo.fr/eric.chopin/pbX_en.htm

This was a test for the admission to a well known

french Engineering School. What was interesting was that

the test contains a question that was unsolved at the

time this examination was given. If someone has the solution,

I'm very interested to know it.

Summary: the goal is to find a solution of

xy''+2y' +x/y=0 defined on [0,1] such that y(1)=e where e is a

given real number. For that purpose one sets g_0=e and

g_{n+1} = e+T(1/g_n) where

T(f)(x) = (1/x-1)\int_0^x t^2f(t)dt + \int_x^1 (t-t^2)f(t)dt

g_{2p} converges to g and g_{2p+1} converges to G. The open

question is to show that g=G ....

Any idea is welcome