REDUCTION METHOD OF HIGHER ORDER DIFFERENTIAL EQUATION SYSTEM TO FIRST ORDERCANONICAL EQUATION SYSTEM IN CAUCHY FORM

HDE system solution by numerical methods of higher order equations results in the input system reduction problem to the 1-st order equation system (Cauchy form). In general case this problem (in a correct statement) has a nonunique solution to be constructed nowadays by sufficiently reliable methods and algorithms. So the solution of the example given below by will-known mathematical packets was unsuccessful.     

Input data: The system of three homogeneous differential equations 

Initial conditions:

Solution:

The method of fulfilment  the solution given below is worked out

Here is a variant of the 1-st order nine equation equivalent system (Cauchy form):

Initial conditions for the system in Cauchy form:

Solution for the 1-st order equation system:

Example 1 (file in Maple 6) -

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