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On the relation between distinct particular solutions of equation

  • Guan Ke-ying (a1) and W. N. Everitt (a1)

Synopsis

There exists a relation (1.5) between any n + 2 distinct particular solutions of the differential equation

In this paper, we show that when and only when n = 0, 1 and 2, this relation can be represented by the following form:

provided the form of this relation function Φn depends only on n and is independent of the coefficients of the equation. This result reveals interesting properties of these non-linear differential equations.

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References

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1Arnold, V. I.. Ordinary Differential Equations (Massachusetts: MIT Press, 1973).
2Mirsky, L.. An Introduction to Linear Algebra (Oxford: Clarendon Press, 1955).
3Petrovski, J. G.. Ordinary Differential Equations (Englewood Cliffs, N.J.: Prentice-Hall, 1966).
4Hille, E.. Ordinary Differential Equations in the Complex Domain (New York: John Wiley & Sons, 1976).
5Baxandall, P. and Liebeck, H.. Vector Calculus (Oxford: Clarendon Press, 1986).
6, Qin Yuanxun. Theory and practice of approximate analytic solutions of ordinary differential equations. Appl. Comp. Appl. Math. 6 (1978), 3554.

On the relation between distinct particular solutions of equation

  • Guan Ke-ying (a1) and W. N. Everitt (a1)

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