# 一阶常微分方程通解中任意常数的分析及教学The Analysis and Teaching of the Arbitrary Constant in the Usual Solution of First Order Ordinary Differential Equation

Abstract: The arbitrary constant of the usual solution to first order ordinary differential equation is discussed in this paper. Firstly, the arbitrary constant in the usual solution does not necessarily take over all of the real numbers. Secondly, the arbitrary constant and special solution is not necessarily a one-to-one correspondence, that is, a constant does not determine a unique special solution, also is not that each special solution can be determined by the arbitrary constant in usual solution. In order to use the method of variation of constant to solve the first order linear differential equation, the canonical form of the usual solution to the homogeneous equation of first order linear differential equation is provided.

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