Stochastic process starting from a Langevin dynamics

Question

I would like to derive a Langevin formulation starting from the definition of a given stochastic quantity (y(t) in my notation, where the first term is a Gaussian noise with zero mean and variance given below, whereas the second is a "memory kernel"). To obtain Eq. (184) for infinitesimal increments in dy I started writing the deviation y(t+\tau)-y(t) and its variance, but I do not know how simplifying Eqs. (186) and (187). Could you please help me? in the attached picture there is an explanation of my computationThank you so much!