Hello people! ;) Here is the problem. Some ideas for analytical solutions of system of equations? Ai constants.

A1*x1''*x2*Cos(x1) - A2*x''*Sin(x1)- A3*x1'' + A4*((x2')^2)*Cos(x1) + A5*Sin(x1)=0

-A6*x1''+A7*x1''*x2*Cos(x1)-A8*x1''*Sin(x1)-A9*((x1')^2)x2*Sin(x1)-A10*((x1')^2)*Cos(x1)+A11=0

We know x1(0), x2(0), x1'(0), x2'(0).

Thank you in advance!

Kind regards!