PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

Commentationes Mathematicae

2007 | 47 | 2 |
Tytuł artykułu

Sur la méthode de l’intégrale particulière et sur ses conséquences pour l’équation de Riccati et pour les équations différentielles linéaires et homogènes d’ordre supérieur

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents the method of particular solution for solving the Riccati equation and linear homogenous equations of second and third order, as well as its certain application to linear homogenous equations of n-th order. The conditions of effective integrability for equations (0.1) and (0.2) are expressed in symbolic (operator) form and also for equation (0.3) in fully expanded form. There have been proved three theorems which state the following: for any subclass of differential equations of the form (0.1), (0.2), (0.3), if there are known, respectively: a particular solution $$y_0$$, a particular solution u 0 , two linearly independent particular solutions $$u_1 , u_2$$, then it is possible to construct superclasses of differential equations of the given class, using classes cited in [6, 7, 8, 9]. Moreover, one may obtain their effectively integrable generalizations. Numerous examples provided illustrate the above results. The article presents also a practical way of applying the method of particular solution to linear equations of n-th order. This method enables us to integrate more general equations than those described in [4, 5, 14] of the form (0.1), (0.2), (0.3), (0.4) for which the particular solutions are cited therein.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Opis fizyczny
Daty
wydano
2007
online
2017-12-19
Twórcy
autor
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory