齐次微分方程(homogeneous differential equation)是指能化为可分离变量方程的一类微分方程,它的标准形式是 y'=f(y/x),其中 f 是已知的连续方程。求解齐次微分方程的关键是作变换 u=y/x,即 y=ux,它可以把方程转换为关于 u 与 x 的可分离变量的方程,此时有 y'=u+xu',代入原方程即可得可分离变量的方程 u+xu'=f(u) ,分离变量并积分即可得到结果,需要注意的是,最后应把 u=y/x 代入,并作必要的变形。
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齐次微分方程组 homogeneous system of differential equations
非齐次微分方程 inhomogeneous differential equation
线性二阶齐次微分方程 linear second-order homogeneous differential equation
线性齐次微分方程 linear homogeneous differential equation
线性非齐次微分方程 nonhomogeneous linear differential equation
齐次微分方程式 equation homogeneous differential
非齐次微分方程式 equation inhomogeneous differential
线性齐次微分方程组 linear homogeneous partial differential equations
齐次线性微分方程 homogeneous linear differential equation
一种重要的情形是常系数二阶线性齐次微分方程。
An important case is the linear homogeneous second-order differential equation with constant coefficients.
权函数是得自对应的齐次微分方程的一般解和完备系。
The weighted functions are obtained based on the use of completed systems of general solution of the corresponding homogeneous equations.
本文给出了一个二阶常系数线性非齐次微分方程的特解公式。
This paper deals with the formula of particular solution to 2-order linear inhomogeneous differential equation with constant coefficients.
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