Application of the Laplace transform to the solution of linear differential equations with variable coefficients

1969 ◽  
Vol 21 (5) ◽  
pp. 538-547 ◽  
Author(s):  
A. G. Shevelev
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
The Laplace Transform ◽  
Linear Differential

The function and associated polynomials

1951 ◽  
Vol 47 (2) ◽  
pp. 309-314 ◽  
Author(s):  
D. F. Lawden
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Difference Equations ◽  
Linear Differential Equations ◽  
Linear Difference Equations ◽  
Transform Method ◽  
Associated Polynomials ◽  
The Laplace Transform ◽  
Linear Differential ◽  
Image Position

A transform method for the solution of linear difference equations, analogous to the method of the Laplace transform in the field of linear differential equations, has been described by Stone (1). The transform u(z) of a sequence un is defined by the equation

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

scholarly journals V. On the calculus of symbols, with applications to the theory of differential equations

1861 ◽  
Vol 151 ◽  
pp. 69-82 ◽  
Keyword(s):  
Differential Equations ◽  
Generating Functions ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
New Methods ◽  
Methods Of Calculation ◽  
Great Utility ◽  
Long Time ◽  
Constant Coefficients ◽  
Linear Differential

The calculus of generating functions, discovered by Laplace, was, as is well known, highly instrumental in calling the attention of mathematicians to the analogy which exists between differentials and powers. This analogy was perceived at length to involve an essential identity, and several analysts devoted themselves to the improvement of the new methods of calculation which were thus called into existence. For a long time the modes of combination assumed to exist between different classes of symbols were those of ordinary algebra; and this sufficed for investigations respecting functions of differential coefficients and constants, and consequently for the integration of linear differential equations, with constant coefficients. The laws of combination of ordinary algebraical symbols may be divided into the commutative and distributive laws; and the number of symbols in the higher branches of mathematics, which are commutative with respect to one another, is very small. It became then necessary to invent an algebra of non-commutative symbols. This important step was effected by Professor Boole, for certain classes of symbols, in his well-known and beautiful memoir published in the Transactions of this Society for the year 1844, and the object of the paper which I have now the honour to lay before the Society is to perfect and develope the methods there employed. For this purpose I have constructed systems of multiplication and division for functions of non-commutative symbols, subject to the same laws of combination as those assumed in Professor Boole’s memoir, and I thus arrive at equations of great utility in the integration of linear differential equations with variable coefficients.

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