1) nomial linear diferential equation
一阶线性微分方程
1.
This paper discusses the application of solving the problem of nomial linear diferential equation with factorization integral.
本文运用因子配导积分法解一阶线性微分方程。
2) first-order matrix linear differential equation
一阶矩阵线性微分方程
1.
This paper deals with the construction of the approximate solution of first-order matrix linear differential equations given by Y′=A(x)Y+B(x) and Y(0)=Y0,where x∈,and A(x),B(x)∈C4,using the quartic matrix spline(QMS).
文章给出了用四次矩阵样条构造形如Y′=A(x)Y+B(x),Y(0)=Y0,x∈[a,b],A(x)、B(x)∈C4[a,b]的一阶矩阵线性微分方程初值问题近似解的方法,研究了该方法的逼近误差并编制了实现该方法的一个算法,最后给出一些数值实例;比较结果表明,用四次矩阵样条所构造的近似解的逼近效果要比用三次矩阵样条所构造的近似解的逼近效果好。
3) linear system of differential equations
一阶线性微分方程组
4) first order nonlinear differential equation
一阶非线性微分方程
1.
In this paper, we generalization of first order nonlinear differential equation of the 1st kind y′P(x)yQ(x)y( μ)R(x)∑ni2f-i(x)yiand obtained the equation such as h′(y)dydxP(x)h(y)Q(x)hμ(y)R(x)∑ni2f-i(x)hi(y)and then research condition of integrability.
将一类一阶非线性微分方程 y′=P(x)y+Q(x)y μ+R(x)+∑ni=2fi(x)yi推广成如下形式 h′(y)dydx=P(x)h(y)+Q(x)hμ(y)+R(x)+∑ni=2fi(x)hi(y)给出了其较为广泛的可积的充分条件,推广并统一了文献[1]和[2]的结论。
5) linear ordinary differential equation of the first order
一阶线性常微分方程
1.
Through preliminary analysis, thorough study and elaborate deduction, the author elucidated the necessity of replacing constant C with function c(x) in solving linear ordinary differential equation of the first order.
文章通过初步说明、深入研究、精确推导三个层次 ,说明了一阶线性常微分方程的常数变易法中把任意常数 C变易成函数 u( x)的内在必然
6) nonliear first order equation
一阶非线性微分方程组
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