Given:
,
solve for y(x) where is a known parameter.
I'm having a hard time doing this - please help!
Using various substitutions, such as
and the sum of angles formula for tangent, I got this down to a 4th degree polynomial in y. This can be solved in theory, so your problem does have a solution, but (as I didn't actually solve the problem) there is a chance that there are no real solutions to this monstrosity. It took me a full 10 minutes before I even saw how to attack this and just as long to come to the realization of what needs to be done. Solving a 4th degree polynomial with constant coefficients is hard enough (I've never actually managed it, the algebra is horrendous), but with the coefficients depending on a complicated formula involving x I'm not going anywhere near this thing. I wish you the best of luck.
-Dan
Thanks very much for your suggestion. Anyway, I came up with these equations while trying to calculate differential cross section for a classical particle scattering of a truncated harmonic potential. If y(x) cannot be found in close form, then one cannot calculate the cross section. This would indeed be sad.