The differential operator of the ordinary
differential equation (ODE) is represented as the sum of two operators: basic
and supplementing operators. The order of the higher derivatives of a basic
operator and ODE operator should coincide. If the basic operator has explicit
system of fundamental solutions it is possible to make integral equation
Volterra of II kind. For linear equations the approximate solutions of the
integral equation are system of the approximate fundamental solutions of the
initial ODE.
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