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