  We apply the topology of convergence on compact sets to define unpredictable
functions [5, 6]. The topology is metrizable and easy for applications with
integral operators. To demonstrate the effectiveness of the approach, the
existence and uniqueness of the unpredictable solution for a delay differential
equation is proved. As a corollary of the theorem, a similar assertion for a
quasilinear ordinary differential equation is formulated. Examples with
simulations illustrate the obtained results.
