scholarly journals Linear Ordinary Differential Equations with Constant Coefficients: Identification of Boole's Integral with that of Cauchy

1960 ◽  
Vol 43 ◽  
pp. 13-15
Author(s):  
D. H. Parsons
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Ordinary Differential Equations ◽  
Constant Coefficients ◽  
Coefficients Identification

scholarly journals Linear Ordinary Differential Equations with Constant Coefficients: Identification of Boole's Integral with that of Cauchy

1960 ◽  
Vol 43 ◽  
pp. 13-15 ◽  
Author(s):  
D. H. Parsons
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Ordinary Differential Equations ◽  
Complementary Function ◽  
Constant Coefficients ◽  
Complex Linear ◽  
Coefficients Identification ◽  
Image Position ◽  
Cauchy's Method

We consider an equation with constant coefficientswhere a≠0 and f(x) is continuous in a suitable interval. Suppose that the symbolic polynomial P(D) has been fully decomposed into its (real or complex) linear factors, so that the equation may be writtenwhere b1, …, bq are distinct, and m1+…+mq = n. The Complementary Function being now known, we may write down a particular integral of (1) by Cauchy's method.

From linear recurrence relations to linear ODEs with constant coefficients

2016 ◽  
Vol 15 (06) ◽  
pp. 1650109 ◽  
Author(s):  
L. Gatto ◽  
D. Laksov
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Ordinary Differential Equations ◽  
Recurrence Relations ◽  
Schubert Calculus ◽  
Linear Recurrence ◽  
Linear Ordinary Differential Equations ◽  
Constant Coefficients ◽  
Linear Odes

Linear Ordinary Differential Equations (ODEs) with constant coefficients are studied by looking in general at linear recurrence relations in a module with coefficients in an arbitrary [Formula: see text]-algebra. The bridge relating the two theories is the notion of formal Laplace transform associated to a sequence of invertibles. From this more economical perspective, generalized Wronskians associated to solutions of linear ODEs will be revisited, mentioning their relationships with Schubert Calculus for Grassmannians.

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