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 ,
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