scholarly journals On the generalized superstability of nth-order linear differential equations with initial conditions

2015 ◽  
Vol 98 (112) ◽  
pp. 243-249 ◽  
Author(s):  
Jinghao Huang ◽  
Qusuay Alqifiary ◽  
Yongjin Li
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Constant Coefficients ◽  
Linear Differential

We establish the generalized superstability of differential equations of nth-order with initial conditions and investigate the generalized superstability of differential equations of second order in the form of y??(x) + p(x)y?(x)+q(x)y(x) = 0 and the superstability of linear differential equations with constant coefficients with initial conditions.

scholarly journals Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 230
Author(s):  
Juan-Carlos Cortés ◽  
Ana Navarro-Quiles ◽  
José-Vicente Romero ◽  
María-Dolores Roselló
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Random Variable ◽  
Second Order ◽  
Singular Points ◽  
Linear Differential Equations ◽  
Transformation Technique ◽  
Order Linear ◽  
Bessel Differential Equation ◽  
Linear Differential

In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.

scholarly journals ELEMENTARY METHOD OF SUBSTANTIATION AND IDEOLOGICAL MEANING OF THE THEORY OF THE SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS AND TRIGONOMETRIC FREE TERMS

2021 ◽  
pp. 105-114
Author(s):  
Zh. A. Sartabanov ◽  
A. Kh. Zhumagaziyev ◽  
A. A. Duyussova
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Teaching Method ◽  
Second Order ◽  
School Mathematics ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Constant Coefficients ◽  
Linear Differential

In the article, adapted to the school course, the second order linear differential equations with constant coefficients and trigonometric free terms are investigated. The basic elementary methodological approaches to solving the equation are given. The solutions of the second order linear differential equation with constant coefficients and trigonometric free terms are investigated, which is a model of many phenomena. In addition, the applied values of the equation and its solutions were noted. The results obtained are presented in the form of theorems. The main novelty of the study is that these results are proved and generalized by elementary methods. These conclusions are proved in the framework of the methods of high school mathematics. This theory, known in general mathematics, is fully adapted to the implementation in secondary school mathematics and developed with the help of new elementary techniques that are understandable to the student. The main purpose of the research is to develop methods for solving a non-uniform linear differential equation of the second order with a constant coefficient at a level that a schoolboy can master. The result will be the creation of a special course program on the basics of ordinary differential equations in secondary schools of the natural-mathematical direction, the preparation of appropriate content material and providing them with a simple teaching method.

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