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 Finance, Statistics & Business Analysisįor the newest resources, visit Wolfram Repositories and Archives ».Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Data Framework Semantic framework for real-world data.
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