Maple Professionel
Maple Académique
Maple Edition Étudiant
Maple Personal Edition
Maple Player
Maple Player for iPad
MapleSim Professionel
MapleSim Académique
Maple T.A. - Suite d'examens de classement
Maple T.A. MAA Placement Test Suite
Möbius - Didacticiels de mathématiques en ligne
Machine Design / Industrial Automation
Aéronautique
Ingénierie des véhicules
Robotics
Energie
System Simulation and Analysis
Model development for HIL
Modélisation du procédé pour la conception de systèmes de contrôle
Robotics/Motion Control/Mechatronics
Other Application Areas
Enseignement des mathématiques
Enseignement de l’ingénierie
Enseignement secondaire et supérieur (CPGE, BTS)
Tests et évaluations
Etudiants
Modélisation financière
Recherche opérationnelle
Calcul haute performance
Physique
Webinaires en direct
Webinaires enregistrés
Agenda des évènements
Forum MaplePrimes
Blog Maplesoft
Membres Maplesoft
Maple Ambassador Program
MapleCloud
Livres blancs techniques
Bulletin électronique
Livres Maple
Math Matters
Portail des applications
Galerie de modèles MapleSim
Cas d'Etudes Utilisateur
Exploring Engineering Fundamentals
Concepts d’enseignement avec Maple
Centre d’accueil utilisateur Maplesoft
Centre de ressources pour enseignants
Centre d’assistance aux étudiants
DEtools[buildsol] - build a solution to an ODE using a reduction of order returned by dsolve and a solution to the reduced ODE
Calling Sequence
buildsol(ODESolStructure, sol_reduced_ODE)
Parameters
ODESolStructure
-
answer returned by dsolve expressed in terms of ODESolStruc
sol_reduced_ODE
solution to the reduced ODE found inside ODESolStruc
Description
For high order ODEs it may happen that dsolve succeeds in reducing the order of the ODE but not in solving the problem to the end. In those cases, the solution is expressed using ODESolStruc. You can obtain a solution for the reduced ODE by using the tools available in DEtools, as a series expansion, or by other means. If a solution to the reduced ODE is obtained, you can build a solution to the original problem using the buildsol command.
The buildsol command is a function of two arguments. The first argument is the structure returned by dsolve as the solution to an ODE (see ODESolStruc). The second argument is a solution found by the user to the reduced ODE present inside the first argument. That solution may be a particular one; buildsol will not check whether the given solution actually solves the reduced ODE.
This function is part of the DEtools package, and so it can be used in the form buildsol(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[buildsol](..).
Examples
A third order nonlinear ODE
This ODE is reducible:
It can be solved by dsolve directly by determining an appropriate integrating factor (see odeadvisor,reducible), but let's consider a possible answer for it as a reduction of order from 3 to 1:
Test that the above solves the ODE by using odetest:
Now, the reduced ODE is of Bernoulli type, and can be selected using the mouse or through the following commands:
From the above, it is clear that a particular solution to the reduced_ODE is given by
from which a particular solution to the original ODE above can be built using
In this "blackboard" example, dsolve succeeds in solving the reduced_ODE too, as follows:
Passing this solution to buildsol, the general solution to ODE follows:
See Also
DESol, DEtools, dsolve, odeadvisor,reducible, ODESolStruc, odetest, PDEtools, series
Download Help Document