Yes, I'm aware it could be solved analytically. My problem lies with the fact that after having changed the entire expression into power series, I'm totally blank on what to do next. The power series for the sine function is complicated relative to the one for y and its derivatives. I'm looking for some way to enable the sine function to be workable. Do you have any hints at least? Or am I looking at an inappropriate way to solve the ODE?
You say you have "changed the entire expression into power series". Please show what you have. The power series for sin x is relatively simple and I would like to see what exactly is giving you trouble. I suspect I know what your difficulty is but I don't want to go into a long-winded explanation if I am wrong.