1) new second order variable coefficient linear differential equation
新二阶变系数线性微分方程
1.
Particularly the solution seeking formula of the two kind new second order variable coefficient linear differential equation are deduced.
提出了一类新二阶非线性微分方程,对它引进特征方程的概念,给出了一个实用的可积充分判据及其通解的积分表述式,在退化情形下,导出了两类新二阶变系数线性微分方程的求解定理,所得结果扩大了常微分方程的求解范围。
2) second order linear non-homogeneous differential equation with variable coefficient
新二阶变系数线性非齐次微分方程
3) variable coefficient linear non-homogeneous differential equation
变系数二阶线性非齐次微分方程
4) second order time variable coefficient linear difficiential equation
二阶时变系数线性微分方程
5) the second order variable coefficient nonhomogeneous linear differential equation
二阶变系数非齐次线性微分方程
6) second order linear differential equation with variable coefficients
变系数二阶线性微分方程
1.
The Solvability of the second order linear differential equation with variable coefficients (y″+)(P(x)y+)(Q(x)y=)f(x) is studied.
利用降阶法研究了变系数二阶线性微分方程y″+P(x)y′+Q(x)y=f(x)的可解性,得到了一个可解的充分必要条件:存在有限形式的可微函数F(x)、G(x),G(x)≠0及常数b和c使得P(x)=bG(x)-G′(x)/G(x)-2F(x),Q(x)=F2(x)-F′(x)-F(x)(bG(x)-G′(x)/G(x))+cG2(x)。
2.
In this paper,a kind of linear differential equation with variable coefficients is turned into second order linear differential equation with constant coefficients through linear and self-variable transformation of unknown function,then a new solvable type of second order linear differential equation with variable coefficients is obtained.
本文通过利用未知函数的线性变换和自变量变换,将一类变系数线性微分方程化成二阶常系数线性微分方程,从而得到变系数二阶线性微分方程的一个新的可解类型。
3.
In this paper, a kind of linear differential equation with variable coefficients is turned into second order linear differential equation with constant coefficients through double transformation——linear and self-variable transformation of unknown function, then a new soluable, type of second order linear differential equation with variable coefficients is obtained.
通过双变换——未知函数的线性变换和自变量变换 ,将一类变系数线性微分方程化为二阶常系数线性微分方程 ,从而得到变系数二阶线性微分方程的一个新的可解类型 ,推广了著名的二阶 Euler方程 。
补充资料：二阶线性齐次微分方程
二阶线性微分方程的一般形式为
ay"+by'+cy=f(1)
其中系数abc及f是自变量x的函数或是常数。函数f称为函数的自由项。若f≡0，则方程（1）变为
ay"+by'+cy=0（2）
称为二阶线性齐次微分方程，而方程（1）称为二阶线性非齐次微分方程。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条