Let Wt; t ϵ [0, 1] be a standard k-dimensional Weiner process defined on a probability space (Ω, F, P), and let Ft denote its natural filtration. Given a F1 measurable d-dimensional random vector X, we look for an adapted pair of processes {x(t), y(t); t ϵ [0, 1]} with values in Rd and Rd×k respectively, which solves an equation of the form: x(t) + ∫t1f(s, x(s), y(s)) ds + ∫t1 [g(s, x(s)) + y(s)] dWs = X. A linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process. We also generalize our results to the following equation: x(t) + ∫t1f(s, x(s), y(s)) ds + ∫t1 g(s, x(s)) + y(s)) dWs = X under rather restrictive assumptions on g.