>"very difficult problem"
>has analytical solution
Thanks, I'll pass.
Admit it, no real problem in this day and age worth giving a single shit for has an analytical solution. Every time another paper gets published about the 12008th obscure way to solve a mere differential equation it is nothing but a waste of time with either no practical application or horrendous real-world accuracy due to the two hundred "approximations" you had to use.
Keep toying with your little ODE and being proud of it, we'll be out here doing actual work with numerical methods.