We study the dynamics of a system of N interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to an interval of length of order ∊ . The interaction is non-negative and scaled in such a way that its scattering length is of order ∊ /N , while its range is proportional to (∊/N ) β with scaling parameter β ∈(0 ,1 ] . We consider the simultaneous limit (N ,∊ )→(∞ ,0 ) and assume that the system initially exhibits Bose-Einstein condensation. We prove that condensation is preserved by the N-body dynamics, where the time-evolved condensate wave function is the solution of a two-dimensional non-linear equation. The strength of the non-linearity depends on the scaling parameter β . For β ∈(0 ,1 ) , we obtain a cubic defocusing non-linear Schrödinger equation, while the choice β =1 yields a Gross-Pitaevskii equation featuring the scattering length of the interaction. In both cases, the coupling parameter depends on the confining potential.