The Integral Equation, Corresponding to the Ordinary Differential Equation
Abstract: 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.
Cite this paper: Dobrovolsky, I. (2014) The Integral Equation, Corresponding to the Ordinary Differential Equation. Open Access Library Journal, 1, 1-5. doi: 10.4236/oalib.1101058.
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