$ (M+2m)\ddot{x} + m(l_1 \ddot{\theta}_1 \cos\theta_1 - l_1\dot{\theta}_1^2 \sin\theta_1) + m(l_2\ddot{\theta}_2 \cos\theta_2-l_2\dot{\theta}_2^2 \sin\theta_2) = F $
$ l_1\ddot{\theta}_1 + \ddot{x} \cos\theta_1 - g \sin\theta_1 = 0 $
$ l_2\ddot{\theta}_2 + \ddot{x} \cos\theta_2 - g \sin\theta_2 = 0 $
Here can I use Cramer's rule to find $\ddot{x}\ or\ \ddot{\theta}_1 \ or \ \ddot{\theta}_2 $ in terms of the $\dot{\theta}_1,\dot{\theta}_2 \ and \ \dot{x}$ ?