二阶常系数线性非齐次微分方程的通解

A General Solution to Order 2 Constant Coefficients Non-homogeneous Linear Differential Equation

在已知二阶常系数齐次微分方程y″+py′+qy=0的一个特解的条件下,讨论了求二阶常系数线性非齐次微分方程y″+py′+qy=f(x)的一个特解的方法,从而根据齐次方程的特征根的不同情形给出了非齐次微分方程的通解公式.

On the basis of a special solution to order 2 constant coefficient homogeneous differential equation y″ ＋ py＇ ＋ qy = 0, a special solution is discussed to order 2 constant coefficient non - homogeneous linear differential equation of y″ ＋ py＇ ＋. qy = f（x）. Following that, the formula of general solution to non - homogeneous differential equation is given.