Introduction to real analysis

What is integration by parts

this article introduces a variation of the parameter method for solving homogeneous linear ordinary differential equations of the second order with constant coefficients, which are most often encountered in the oil and gas engineering when studying the drilling, production and pipeline transport of oil and gas. In addition, we derive a general method of solution for solving homogeneous linear ordinary differential equations of the second order with constant coefficients. Keywords— differential equation; the equation of oscillations; linear combination; oil and gas industry, drill pipes.

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Peculiarities of problem solving at studying well drilling with the use of linear differential equations with constant coefficients

Differential equations of engineering science

Higher-Order Linear Ordinary Differential Equations

In this manuscript, we introduce variation of parameter method for solving homogeneous linear second order ordinary differential equations with constant coefficients. Moreover, we derive general solution method to solve homogeneous linear second order ordinary differential equations with constant coefficients.

Variation of Parameter Method for Solving Homogeneous Second Order Linear Ordinary Differential Equations

In this paper, we derive equivalent equations of integration of secant and cosecant functions. Furthermore, we derive reduction formula for integration of product of integer powers of cosine and sine functions.

A Note on Integration of Trigonometric Functions

Most authors of differential equations used integrating factor to solve linear first order ordinary differential equations. In this paper, we introduce undetermined functions method to solve linear first order ordinary differential equations. Moreover, we derive solution method for solving linear first order ordinary differential equations without applying exactness condition.

Undetermined Functions Method for Solving First Order Differential Equations

In this manuscript, we introduce Geo*Arithmetic Series. Mainly, we use theories and theorems on series to find partial sum of Geo*Arithmetic Series. Moreover, we show a Geo*Arithmetic Series is convergent (divergent) series whenever the absolute value of the common ratio of its terms is less than one (greater than one). Furthermore, we find the sum of a Geo*Arithmetic Series whenever the absolute value of the common ratio of its terms is less than one.

Introduction to Geo*Arithmetic Series

In this paper, we introduce higher integral of differential equations. Also, we solve some higher integral of differential equations. Moreover, we show all solutions of some higher integral of differential equations are also solutions of those differential equations.

Daniel Arficho

Papers

Variation of Parameter Method for Solving Homogeneous Second Order Linear Ordinary Differential Equations

A Note on Integration of Trigonometric Functions

Undetermined Functions Method for Solving First Order Differential Equations

Introduction to Geo*Arithmetic Series

Introduction to Higher Integral of Differential Equations