Authors use the method combining the operation with figure, analyzing the convergent solutions of the cubic positive coefficient homogeneous differential equation, drawing the three categories of curves by the discriminant △＞0, △=0, △＜0 , which perceived directly when △=0, △＜0 the characteristic equation has negative real roots and the solution is convergent, but when △＞0 it has a couple of conjugate complex roots, when the real part of roots α'≥0, the solution is divergent. In view of this situation the authors indicate that two uncertified constants in the solution must tend to zero, relevantly, the thesis discusses completely how to find the convergent solutions in general and modifies the normal statement about discriminant △=0 in the mathematic handbooks also.%用数形结合的方法,对三阶正系数齐次微分方程的收敛解进行了讨论,由特征方程的求根判据描绘出△＞0、△=0、 △＜0三类图形.当△=0、△＜0时方程具有负实根,其解收敛;△＞0时方程具有共轭复根,当实部α'≥0时其解发散.然而,物理原理和现实规定其解必须收敛,对此,提出了此时解中的两个不定常数应该趋零,解产生退化.对如何从一般解中挑选出收敛解作了完整的分析,并且对辞典中△=0时三次方程的求根判据的一般叙述作了改进.
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