Analytic Solution for Ramsey Optimal Saving Problem

What kinds of utility and production function leads to an analytic solution of policy function(the saddle path) in continuous time version? Thanks!

Start with https://www.researchgate.net/publication/4744308_A_Closed_Form_Solution_to_the_Ramsey_Model and the references therein.

Thank you very much! You have completely solved my problem!