Reduction of the Ordinary Linear Differential Equation of the nTH Order Whose Coefficients are Certain Polynomials in a Parameter to a System of n First-Order Equations Which are Linear in the Parameter

1927 ◽  
Vol 29 (3) ◽  
pp. 497
Author(s):  
Charles E. Wilder
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Ordinary Linear Differential Equation ◽  
First Order ◽  
Linear Differential

Studies in multiplicative solutions to linear differential equations

1987 ◽  
Vol 106 (3-4) ◽  
pp. 277-305 ◽  
Author(s):  
F. M. Arscott
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Floquet Theory ◽  
Special Functions ◽  
Linear Differential Equations ◽  
Ordinary Linear Differential Equation ◽  
Closed Path ◽  
Starting Point ◽  
Linear Differential

SynopsisGiven an ordinary linear differential equation whose singularities are isolated, a solution is called multiplicative for a closed path C if, when continued analytically along C, it returns to its starting-point merely multiplied by a constant. This paper first classifies such paths into three types, then investigates combinations of two such paths, in which a number of qualitatively different situations can arise. A key result is also given relating to a three-path combination. There are applications to special functions and Floquet theory for periodic equations.

scholarly journals Possible Contamination from Rainwater in Community Pool

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
David McGregor
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Linear Differential Equation ◽  
Organic Contaminants ◽  
Organic Pollutant ◽  
Swimming Pool ◽  
Ordinary Linear Differential Equation ◽  
Initial Condition ◽  
Linear Differential ◽  
Specific Equation

The project is meant to create an equation that can be used to estimate the amount of organic pollutant – bacteria - that is present in a swimming pool per day from rainwater. This equation is derived through a differential equation of the rate in minus the rate out. The created differential equation is an ordinary linear differential equation and is solved using an integration factor. The general solution is then converted into a specific equation using an initial condition. The resulting equation provides an approximate number of organic contaminants x(t) present in the pool after an amount of time in days (t). The equation finds that the pool – during its closure – has been cleaned often enough. It also provides a method to estimate the amount of contamination from rain after any other extended closures.

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