CONSTRUCTION METHOD 

OF LINEAR DIFFERENTIAL EQUATIONS AND SYSTEMS 

ON PREASSIGNED SOLUTION IN QUASIPOLYNOMIAL CLASS


It is known that the linear homogeneous differential equation (HDE) solution with constant coefficients can be only quasipolynomial. Therefore the function class for the formulated problem to be solved is restricted by a complex quasipolynomial class. For the general case the given problem has the uncountable set of solutions. However if it is necessary for the desired equation order to be minimal, HDE – standardized (coefficient in higher derivative is real and equals to unit) and the argument of initial representation conditions – zero, then the problem (in this case) has the unique solution.

The method, the algorithm and the solution program of the formulated problem are worked out

EXAMPLE 1. Let HDE be constructed for the following solution:

The constructed HDE is a 8-th order equation (calculation time is 1.2 sec.):

The constructed initial conditions:

     

 - example 1 (file in Maple 6)

 - example 2 (file in Maple 6)

                                                                                                  

The obtained HDE and the initial conditions correspond to the input quasipolynomial with a high precision. We can be easily convinced of this by solving the found equation with the help of the mathematical Maple

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