of the ode system is returned as two-dimensional array where the first column (sol[:, ]stores and the second (sol[:, ]stores plotting and is matter of running plot(tutvremark in the right-hand side function we write (soltomegainstead of (utomegato indicate that the solution sent to is solution at time where the values of and are packed togethersol [uvwe might well use as argumentdef (utomega= )uv return [ -omega** *uthis just means that we redefine the name inside the function to mean the solution at time for the first component of the ode system to switch to another numerical methodjust substitute rk by the proper name of the desired method typing pydoc odespy in the terminal window brings up list of all the implemented methods this very simple way of choosing method suggests an obvious extension of the code abovewe can define list of methodsrun all methodsand compare their curves in plot as odespy also contains the euler-cromer schemewe rewrite the system with as the first ode and as the second odebecause this is the standard choice when using the euler-cromer method (also in odespy)def (utomega= )vu return [-omega** *uvthis change of equations also affects the initial conditionthe first component is zero and second is x_ so we need to pass the list [ x_ to solver set_ initial_condition the code osc_odespy py contains the detailsdef compare(odespy_methodsomegax_ number_of_periodstime_intervals_per_period= )from numpy import pilinspacecos *pi/omega length of one period dt /time_intervals_per_period number_of_periods*