Is this differential system of equations *coupled*?

[asgard]

I am struggling with whether or not to define the following system as coupled:
Using LaTeX (reload if it doesn't display properly)

\ddot{x}+A*x=0

\ddot{y}+A*y=0

\ddot{z}+A*z=0​

where A is a known constant equal to A=\sqrt{x^2+y^2+z^2}

So, what do you think?

 

[LCKurtz]

Yes, it is a coupled system. Even if A is constant so the solution is apparently restricted to a sphere, still the value of x depends on y and z. I don't 100% guarantee this answer though.

 

[HallsofIvy]

Yes, these equations are coupled.