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4.1 Basic Concepts. Classification of Linear Differential
Equations…………………………………………….....……..61
4.2 Linear Dependence and Linear Independence of
Systems of Functions…………………………………….........62
4.3 Linear Homogeneous Differential Equations…........64
4.3.1 Wronski-Determinante………………………..……64
4.3.2 Structure of Common Decision of LHDE………...67
4.4 Linear Heterogeneous Differential Equations……....70
4.4.1 Structure of Common Decision of Linear
Heterogeneous Differential Equation………………………....70

Lecture 5 Solving of Homogeneous Linear Differential
Equations (LHDE) with Constant Coefficients……………….74

5.1 Linear homogeneous differential Equations with
Constant Coefficients………………………………………....74

5.1.1 Characteristic Equation………………………….…74
5.1.2 The Roots of Characteristic Equation Real and
Simple………………………………………………………....75
5.1.3 The Roots of Characteristic Equation are Real
multiple………………………………………………….….…76
5.1.4 The roots of Characteristic Equation Are Complex
Conjugate…………………………………………………..….78
5.1.5 The roots of Characteristic Equation are
Arbitrary…………………………………………………..….80

Lecture 6 Solving of Heterogeneous Linear Differential
Equations (LNDE) With Constant Coefficients……………...83

6.1 Method of variation………………………………....83
6.2 Linear Heterogeneous Differential Equations of the n-th
Order With Constant Coefficients and Special Type of the Right
Part……………………………………………………………87
6.3 Linear Heterogeneous Differential Equations of the
Second Order With Constant Coefficients…………………....93
6.4 Principle of superposition of decisions……………....98

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