scholarly journals Integrability of Planar Polynomial Differential Systems through Linear Differential Equations

2006 ◽  
Vol 36 (2) ◽  
pp. 457-485 ◽  
Author(s):  
H. Giacomini ◽  
J. Giné ◽  
M. Grau
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Linear Differential ◽  
Planar Polynomial Differential Systems

Generalized systems of linear differential equations

1981 ◽  
Vol 89 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
Rainer Pfaff
Keyword(s):  
Differential Equations ◽  
Bounded Variation ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Generalized Systems ◽  
Linear Differential ◽  
Derivatives Of

SynopsisWe consider ordinary linear differential systems of first order with distributional coefficients and distributional nonhomogeneous terms. Firstly the coefficients are assumed to be functions, secondly to be first order distributions (i.e. first derivatives of functions which are integrable or of bounded variation), and thirdly to be distributions of higher order.

V.—On the Connexion between Linear Differential Systems and Integral Equations

1923 ◽  
Vol 42 ◽  
pp. 43-53 ◽  
Author(s):  
E. L. Ince
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Integral Equations ◽  
Green's Function ◽  
Linear Differential Equations ◽  
Differential Systems ◽  
Definite Integrals ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
The Relationship

This paper summarises the results of an attempt to extend the theory upon which the relationship between linear differential equations and integral equations is based. The case in which the nucleus K(x, s) of the integral equation arises as a Green's function is well known; the nucleus is there characterised by its having discontinuous derivates when x = s. The method here dealt with is virtually an extension of Laplace's and analogous methods for solving linear differential equations by definite integrals, and leads to nuclei which are continuous and have continuous derivates for x = s.

scholarly journals On the Composition of Simultaneous Differential Systems of the First Order

1932 ◽  
Vol 3 (2) ◽  
pp. 128-131
Author(s):  
M. Mursi-Ahmed
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Differential Equations ◽  
Differential Systems ◽  
Order Linear ◽  
First Order ◽  
Linear Differential ◽  
Image Position

§ 1. Consider the system of n first order linear differential equations:together with the n boundary conditionswhere aij, bij are constants and where we assume for simplicity of notation that gii = 0.

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