Thank you!
I did my math by myself and verify your solution, although I searched solution in the form x(t)=x_0e^{i\omega{t}}, so it's just a matter of adding an imaginary unit here and there. It's now clear to me, why one cannot drop fourth derivative - when dealing with rotating reference...
Context: problem I need to solve is about pendulum in a rotating frame
Well, I already dropped all components that are Big O(angle ^3) and beyond in Lagrangian, for the sake of finding analytic solution (otherwise I'd have system of three coupled 2nd order diff equation with variable...
Thanks, worked.
But it's strange that equations for x and y have both the same solution (although it shouldn't). I dropped fourth order derivative and solved second order ODE.
Case closed for now.
I have to derive equations of motion from Lagrangian and stumbled upon the following system of equations (constants are simplified, that information is unneeded)
\begin{cases}
\ddot{x}-A\dot{y}+Bx=0 \\
\ddot{y}+A\dot{x}+Dy=0
\end{cases}
This is an extension of a simpler problem where B=D...