What are the ODEs for a vehicle in motion under gravitational pull?

[Ry122]

I'm attempting to find a system of ODEs for a vehicle in motion that undergoes acceleration due to the gravitational pull of different bodies in space.
It has an initial velocity, but doesn't undergo any change in acceleration due to thrust.

This vector represents its motion.
http://img834.imageshack.us/img834/2161/vecth.jpg
x and y accelerations are represented by:
http://img805.imageshack.us/img805/3908/accel.jpg
I'm asked to find the first order system of ODEs and it needs to be written in the form:
http://img411.imageshack.us/img411/3246/formh.jpg
I know that velocity and displacement can be found by integrating acceleration once and twice but I'm not really sure how to go about determining ODEs as a function of a state vector

 

[lippyka]

.The system of ODEs can be written as follows: dx/dt = vx dvx/dt = ax dy/dt = vy dvy/dt = ay Where ax and ay are the x and y components of acceleration due to the gravitational pull of different bodies in space, and vx and vy are the x and y components of velocity.