Reference for the differential equation $(\ddot{x}(t), \ddot{y}(t))=-G/r^3(x(t), y(t))$?

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Does anyone know where I can find the deduction of the differential equation

$$(\ddot{x}(t), \ddot{y}(t))=\frac{-G}{r^3}(x(t), y(t))$$

where $t\mapsto (x(t), y(t))$ describes the moviment of a body in a plane around a spherical mass? Here $G$ is a constant (should be the gravitational constant) and $r$ is the distance from the sphere.

Thanks.