In this manuscript we focus on a system of differential equations that describes the trajectory of a particle that moves in the plane according to a hypocycloid curve. More precisely we consider a coupled system composed of two ordinary second order differential equations with initial conditions given by interactive fuzzy numbers. The concept of interactivity is given by means of joint possibility distribution (J). We provide a fuzzy solution for this system via sup- J extension, which can be seen as a generalization of the Zadeh's extension principle. We present an example in order to compare the proposed solution with the solution via Zadeh's extension principle.