  We present a condition for a stochastic differential equation
dX_{t}={\mu}(t,X_{t})dt+{\sigma}(t,X_{t})dB_{t} to have a unique functional
solution of the form Z(t,B_{t}). The condition expresses a relation between
{\mu} and {\sigma}. A generalization concerns solutions of the form Z(t,Y_{t}),
where Y_{t} is an Ito-process satisfying a stochastic differential equation
with coefficients only depending on time, to be determined from {\mu} and
{\sigma}. The solutions in question are obtained by solving a system of two
partial differential equations, which may be reduced to two ordinary
differential equations.
