Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient

1975 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Second Order ◽  
Linear Ordinary Differential Equation ◽  
Polynomial Coefficient ◽  
Global Theory ◽  
Order Linear

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

scholarly journals General Solution Of Nth-Order Linear Ordinary Differential Equation

2021 ◽  
Author(s):  
Rajnish Kumar Jha
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
General Solution ◽  
Linear Ordinary Differential Equation ◽  
Order Linear ◽  
Special Case ◽  
Integrating Factors

In this paper we present a solution expression for the general Nth-order linear ordinary differential equation as our main result which involves the use of Integrating Factors where the Integrating Factors are determined using a set of equations such that when this set of equations can be solved, the solution of the concerned differential equation can be determined completely. In this regard we also present result for a special case corresponding to the main result where the solution of the general Nth-order linear ordinary differential equation can be determined completely when N-1 out of N complementary solutions are known.

scholarly journals General Solution Of Nth-Order Linear Ordinary Differential Equation With Constant Coefficients

2021 ◽  
Author(s):  
Rajnish Kumar Jha
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
General Solution ◽  
Linear Ordinary Differential Equation ◽  
Order Linear ◽  
Constant Coefficients

In this paper we present a formula for the general solution of Nth-order linear ordinary differential equation with constant coefficients as our main result. In this regard we also present two supporting results in this paper which reduce the order of the concerned differential equation by one and give the relation between the coefficients of the initial differential equation and the differential equation obtained. We also discuss about the complementary solution and homogeneous equations with regard to the main result described in this paper.

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