Computation of differential equation particular solutions with application to sigma plots

1984 ◽  
Vol 29 (5) ◽  
pp. 457-459
Author(s):  
J. Broussard
Keyword(s):  
Differential Equation ◽  
Particular Solutions

scholarly journals An application of Ritt’s low power theorem

1977 ◽  
Vol 68 ◽  
pp. 17-19 ◽  
Author(s):  
Michihiko Matsuda
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Low Power ◽  
Singular Solution ◽  
Algebraic Differential Equation ◽  
Classical Concept ◽  
First Order ◽  
Particular Solutions ◽  
Rigorous Definition ◽  
Particular Solution

AbstractConsider an algebraic differential equation F = 0 of the first order. A rigorous definition will be given to the classical concept of “particular solutions” of F = 0. By Ritt’s low power theorem we shall prove that a singular solution of F = 0 belongs to the general solution of F if and only if it is a particular solution of F = 0.

scholarly journals Explicit Solutions of Singular Differential Equation by Means of Fractional Calculus Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Resat Yilmazer ◽  
Okkes Ozturk
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Ordinary Differential Equations ◽  
Explicit Solutions ◽  
Singular Differential Equation ◽  
Linear Ordinary Differential Equations ◽  
Particular Solutions ◽  
Fractional Calculus Operators

Recently, several authors demonstrated the usefulness of fractional calculus operators in the derivation of particular solutions of a considerably large number of linear ordinary and partial differential equations of the second and higher orders. By means of fractional calculus techniques, we find explicit solutions of second-order linear ordinary differential equations.

The distribution of temperature along a thin rod electrically heated in vacuo II. Theoretical (continued)

1954 ◽  
Vol 225 (1160) ◽  
pp. 1-7 ◽  
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Particular Solutions ◽  
Long Rod

For a thin rod electrically heated in vacuo the differential equation defining the distribution of temperature in the steady state has been formulated previously. If the rod is not too short, a solution can be obtained by suitably combining the two particular solutions for a similar infinitely long rod heated by the same current, which is applicable over the whole length of the rod. The solution is discussed in relation to some formulae that had been proposed by Stead. The solution also leads to a very useful expression for the temperature at the centre of a finite long rod as a function of its length.

On the relation between distinct particular solutions of equation

1993 ◽  
Vol 123 (5) ◽  
pp. 917-926
Author(s):  
Guan Ke-ying ◽  
W. N. Everitt
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Particular Solutions ◽  
Non Linear ◽  
Linear Differential ◽  
Image Position

SynopsisThere exists a relation (1.5) between any n + 2 distinct particular solutions of the differential equationIn this paper, we show that when and only when n = 0, 1 and 2, this relation can be represented by the following form:provided the form of this relation function Φn depends only on n and is independent of the coefficients of the equation. This result reveals interesting properties of these non-linear differential equations.

Differential equation for a stratified fluid and its particular solutions

1987 ◽  
Vol 21 (5) ◽  
pp. 746-750
Author(s):  
A. Yu. Yakimov ◽  
Yu. L. Yakimov
Keyword(s):  
Differential Equation ◽  
Stratified Fluid ◽  
Particular Solutions

EXPLICIT SOLUTIONS TO THE KAUP–KUPERSHMIDT EQUATION VIA NONLOCAL SYMMETRIES

2007 ◽  
Vol 17 (08) ◽  
pp. 2749-2763 ◽  
Author(s):  
ENRIQUE G. REYES ◽  
GUILLERMO SANCHEZ
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Scattering ◽  
Infinite Number ◽  
Hamiltonian Formulation ◽  
Explicit Solutions ◽  
Nonlocal Symmetries ◽  
Particular Solutions ◽  
Generalized Symmetries ◽  
Fifth Order

The fifth order Kaup–Kupershmidt equation [Formula: see text] is a most important example of an integrable partial differential equation. Among other properties, it is integrable via scattering/inverse scattering techniques, it admits a bi-Hamiltonian formulation, and it possesses an infinite number of generalized symmetries. In sharp contrast with other integrable equations, however, it has proven very difficult to exhibit explicit solutions to Kaup–Kupershmidt. In this paper, we present several interesting particular solutions to this equation obtained with the help of nonlocal symmetries.

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