x^y=y^x
x^x=y^(9y)
I need this in next few hours please help
You're right. I should have remembered that the only integer solutions of are (2, 4) and (4, 2) .....
So (9, 3) is a spurious solution ......
If you sub x = 3y into you get:
.
An approximate solution is . This solution does seem to work ..... To express this solution for y in exact form, I think you'd need to use the Lambert W-function ......
I haven't looked at the x = -3y case yet, but there will probably be similar if not worse difficulty in store ......
Are you expected to get exact solutions?