4 semester


Course title

Differential equations


Year of study,

study programme


1-31 03 08 Mathematics and Information Technologies


Semester of study



Number of credits




Roudenok Alexander Evgenievich


Course Objective

The purpose of studying the discipline is to train specialists possessing the knowledge and skills to use effectively the basic methods of the theory of differential equations to study the phenomena and processes of reality surrounding us.

Studying the discipline solves the following tasks:

– acquisition by students of knowledge in the field of the theory of differential equations;

– Acquisition of practical skills in solving mathematical problems, constructing and analyzing mathematical models described by differential equations.

As a result of the training, the student must


– techniques for integrating linear differential equations and systems;

– formulation of the Cauchy problem for linear differential equations and systems;

– statement of boundary value problems;

– existence and uniqueness theorems;

– Lyapunov stability notion and Lyapunov’s stability theorem;

– basic concepts of the theory of autonomous differential equations on the plane;

     be able to:

 – solve linear differential equations and systems;

– set the Cauchy problem and solve it;

– to set boundary-value problems and solve them;

– determine the stability of solutions of autonomous systems and their singular points;


– the main methods of constructing differential models of real phenomena and processes.



Algebra. Mathematical analysis. Geometry.


Course content

A homogeneous linear DE of order n. An inhomogeneous linear DE of order n. Method of variation of arbitrary constants. A homogeneous linear DE of order n with constant coefficients. Euler’s method. Volebility of solutions of a linear DE of order 2. Boundary problems. Systems of linear differential equations of the first order. Homogeneous systems of linear differential equations of the first order. Inhomogeneous system of first-order linear differential equations. Homogeneous linear system with direct coefficients. Euler’s method. Method of variation of arbitrary constants A matrix exponent. A matrix method for solving a homogeneous linear system of DE with constant coefficients. Autonomous remote control systems in the plane. Stability by Lyapunov. Singular points of an autonomous remote control system on a plane.


Recommended Literature

1.Филиппов, А.Ф. Введение в теорию дифференциальных уравнений: учебник / А.Ф.Филиппов.-М.: Едиториал УРСС, 2004.-240 с.

2.Амелькин, В.В. Дифференциальные уравнения:  учеб.пособие / В.В.Амелькин.-Минск: БГУ, 2012.-288с.

3.Федорюк, М.В. Обыкновенные дифференциальные уравнения: учеб.пособие. Изд.2-е / М.В.Федорюк.-М.: Наука, 1985.-448 с.


Teaching Methods

Explanatory-illustrative, reproductive, partially-search


Teaching language



Requirements, current control

Test papers. Exam score consist of the current mark (40%) and the oral exam mark (60%).


Method of certification