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Lecture 7 Systems of Differential Equations

7.1. Common Notions on Systems of Differential
Equations

In the process of solving of many scientific and technical
tasks there is the necessity of study of a few interposes
communication or cases, when the sought function after is a
vector, that results in solving of not alone differential Equation,
and systems of such equations.
Example 7.1 Equation of motion of some object in a vector
form is:

dv  
m  F ( , , , )x y v t ,
dt

  dx  dy   
where v  i  j  speed, F  iX  jY  is an external
dt dt
force.

 Designing this correlation on the axis of coordinates, we
get the system of differential equations:

2
 d x  dx dy 
,


 m dt 2  X t , , ,x y dt dt  ,
 2   (7.1)


 m d y  Y t , , ,x y dx dy  .
,
 dt 2   dt dt  


In future we will be limited to consideration of the so called
canon systems, in which all equations are untied relatively
senior derivative. The canon system always can be replaced by
the system of equations of the first order equivalent to her, and
the number of equations of which equals the sum of orders of
equations of the initial system.
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