This paper studies numerical methods that are used to treat ordinary differential equations arising in extended Kalman filtering algorithms. Such problems are called the moment equations and constitute an important subclass of differential equations. They all possess a number of specific properties that make the standard available software ineffective for some mathematical models in this area. For instance, we show that built-in Matlab ODE solvers are not able to cope with a number of tests considered here. In contrast, the hybrid method developed by Mazzoni (2007) exhibits much better performance on the same examples. The latter means that specially designed numerical schemes are needed for efficient solution of the moment equations instead of the standard software designed for general systems of ordinary differential equations.