The MATLAB command ode45 performs a direct numerical integration of a set of differential equations y' = f(t,y), y(to)=yo from to to some final time tf. See "help ode45" for a more detailed explanation.
The "45" part specifies the type of numerical integration used. There are others (ode23, ode113, ode15s, ode23s, ode23t, ode23tb); ode45 is a general-purpose solver. For the gory details, see the associated MATLAB Function Reference.