Unpredictable solutions of differential equations

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.