【摘要】 为研究n阶常系数非齐次线性常微分方程解的问题,求证了n阶常系数非齐次线性常微分方程的通解和特解的积分表达式.利用韦达定理和一个变量替换,对n阶常系数非齐次线性微分方程进行降阶,导出该方程的一个用积分表示的通解公式,并根据特征根的不同情形给出了通解的各种形式及相应的通解和特解公式.更多还原

【Abstract】 To obtain the general solution and their special solutions in integration form,the way to get the n order non-homogeneous linear ordinary equation with constant coefficients was studied.Resorting to the theory of Vieta and an alternative transformation,the order of the equation is lowered and a general solution formula,expressed by integrations was derived.According to root cases of the auxiliary equation,the detailed expressions of the general solution and their special solutions were given.更多还原