Wolfram Mathematica 2022 is a full-featured suite which brings together calculations, solution, graphics and text in a single electronic document. SolvingHigherOrderODEsMathematica52April272005.nb (164.It provides over 6,000 built-in functions covering all areas of technical computing, all carefully integrated so that they work perfectly in the fully integrated Mathematica system.
Mathematics > Calculus and Analysis > Differential Equations We end this introduction by noting that it will be convenient to switch back and forth between (homogeneous) differential equations and the corresponding differential operators since the algorithms really refer to the differential operators and the final step of integrating lower order ODEs to find the solutions is straightforward in all cases. In Section 5, we deal with the important notion of factorization for a differential operator. Section 4 deals with a generalization of the notion of symmetric power in which we start with a pair of second order ODEs. In Section 3, we will discuss the implementation of the Bronstein-Mulders-Weil-van Hoeij algorithm for solving linear ODES of arbitrary order that are symmetric powers of second order ODEs. In Section 2, we will review the methods for solving higher order ODEs which were already available in V 5.1. Thus, we were interested in widening the application of the methods implemented in Version 5.1 to higher order ODEs. Also, higher order ODEs (particularly orders 3 and 4) are increasingly being seen in scientific models. Within the last few years, a deeper understanding of several aspects of higher order ODEs (such as factorization techniques) has emerged which makes it possible to carrry out this reduction in a systematic way.
As explained in the Advanced Documentation for DSolve, the code structure for this function is hierarchical, so that the problem of solving ODEs of order greater than 2 is often reduced to that of solving a first order or second order ODE. In Mathematica 5.1, we had focussed on adding methods for solving first order and second order ODEs such as Abel equations, hypergeometric-type equations and equations with non-rational coefficients using DSolve. The aim of this notebook is to explain the motivation for these developments and to provide some information and examples which illustrate the new functionality.
The Mathematica function DSolve has been equipped with several modern algorithms for solving higher order linear ordinary differential equations (ODEs) in Version 5.2. Solving Higher Order ODEs using Mathematica 5.2
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