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Earth geopotential effect on orbit propagation

I'm trying to take into account the Earth geopotential effect on the orbit. The only term I could consider, is J2.

  1. Are the terms (J2, etc.) change with time?
  2. I found other terms coefficients here. How to add them also to differential equation?

    enter image description here

The shown equation gives 1 km error in comparison with GMAT, where degree 2 and order 0 is chosen for JGM-3 model. Is it due to the change of the term with time, which I didn't consider?