There exists a positive real number such that
has solutions with
and
for all
in the open interval
. Compute the value of
and find all solutions of the equation.
Since is a solution of
we know
for some constants and
. We are given
,
Therefore,
with (since if
then
for all
contradicting that
on
). Therefore,
for . (We know
since
.)
Then, since on
, we know
, otherwise
would change sign on the interval. Hence,
and the solutions are