Hello everybody!

A problem:

Find functions which are fulfilling:

for all .

Prove that if are fulfilling the above equation then determined by . How?

Thank you.

Results 1 to 5 of 5

- May 26th 2011, 04:18 AM #1

- May 26th 2011, 04:26 AM #2

- May 26th 2011, 04:59 AM #3

- May 27th 2011, 07:45 AM #4
This is how I might attempt to do this problem. I will assume that both and are smooth. Taking the natural log of both sides gives

.

Call the term on the RHS . Differentiating both side wrt and gives

.

Thus, where and are constant.

So

so .

Now set and this gets you the form for Then substitute into the original functional equation to determine .

- May 29th 2011, 02:05 PM #5