newtonian mechanics - Foucault pendulum

The equations of motions for a Foucault pendulum are given by:

$$\ddot{x} = 2\omega \sin\lambda \dot{y} - \frac{g}{L}x,$$ $$\ddot{y} = -2\omega \sin\lambda \dot{x} - \frac{g}{L}y.$$

What are the equations describing $\dot{x}$ and $\dot{y}$?