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CONTEXT

Lecture 1 Notion of Ordinary Differential Equations……..6

1.1 Common Notions and Determinations...........................6
1.2 Solving Cauchy Task and Its Geometrical
Interpretation………………………………………………....…8
1.3 Solving of Some Equations of the First Order, Untied in
Relation to Derivative…………………………………………11
1.3.1 Equation with the Separated and Separated Variables
and Panders to Them………………………………………….12

Lecture 2 Solving of Some Equations of the First Order,
That Get Untied in Relation to Derivative……………..…….17

2.1 Equation in Complete Differentials Equation….…….17
2.2 Method of Integrating Cofactor………………........…20
2.3 Homogeneous Equations………………………….….24
2.3.1 Equations That Are Taken to Homogeneous…….....28
2.4 Linear Differential Equations of the First Order….….32
2.5 Bernoulli Equation………………………………..…..39

Lecture 3 Differential Equations of Higher Orders….…..46

3.1 Common Notions and Determinations…………….…46
3.2 Differential Equations of Higher Orders Which Assume
the Decline of Order…………………………......................…49
(n)
3.2.1 Equations of a Kind y =f(x)…………………......49
3.2.2 Differential Equations of a Kind
(k ) ( k ) 1 (n )
F (x , y , y ,...,y )  0…………………………….……51
3.2.3 Differential Equation of the Kind
F (y ,  y ,  y ,..., y (n ) )  0 …………………………………...…...56

Lecture 4 Linear Differential Equations of Higher Orders
(elements of general theory)…………………………….…….61

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