**Functions in use for solving ordinary differential equations in Mathcad**

In order to solve ordinary differential equations and sets of ordinary differential equations Mathcad offers a number of functions:

**odesolve(x,b,step)**is used for solving the ordinary differential equation, assigned either in form of Cauchy problem or in form of the boundary-value problem. Initial conditions and the differential equation are to be settled in case**given.**Function parameters:**х**–variable for integration;**b**– finite value of solution interval;**step**– stride parameter of the numerical procedure (not compulsory).**rkfixed(u,a,b,N,D)**realizes in Mathcad the numerical procedure for Cauchy problem using Runge-Kutta method with the fixed stride (step). Takes advantage over**odesolve(x,b,step)**in the following: can be used in programme packages and lets recount the results immediately in case of any parameter change. Function parameters:**u**-initial conditions vector;**a**и**b**– boundary values of problem solution interval;**N**– number of intervals fragment**[a,b]**is divided into**; D(x,y)**–vector-function, containing the right segments of the first derivatives, written down in a character way.**Rkadapt(u, a,b, N, D)**– returns matrix in Mathcad, which contains the value table of Cauchy problem solutions at the interval from a to b for the equation or the set of differential equations, calculated with Runge-Kutta method with the variable stride (step) and initial conditions in vector**u, D(x,y)**–vector-function, containing the right segments of the first derivatives, written down in a character way,**n**– number of strides (steps).- Function
**Rkadapt()**due to the automatic selection of strides normally gives a more accurate result in comparison with other Mathcad functions.

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