  In this note, we formulate a ``one-sided'' version of Wormald's differential
equation method. In the standard ``two-sided'' method, one is given a family of
random variables which evolve over time and which satisfy some conditions
including a tight estimate of the expected change in each variable over one
time step. These estimates for the expected one-step changes suggest that the
variables ought to be close to the solution of a certain system of differential
equations, and the standard method concludes that this is indeed the case. We
give a result for the case where instead of a tight estimate for each
variable's expected one-step change, we have only an upper bound. Our proof is
very simple, and is flexible enough that if we instead assume tight estimates
on the variables, then we recover the conclusion of the standard differential
equation method.
