We shall show sufficient and necessary condition that first order differential equation M(x,y)dx+N(x,y)dy=0 have 1,μ(x,y)=F(ax+by),2,μ(x,y)-G(xy), 3,μ(x,y)=exp[∫f(x)dx+∫g(y)dy] three forms integrating factors.
The second-order N-dimensional radial Schrdinger differential equation with the isotropic harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform, and then, its solutions are directly obtained by means of making use of an integral.
The second-order one-dimensional Schrdinger differential equation for the harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform,and then,its solutions are obtained by means of directly making use of an integral.
Master equations which normally appear as an infinite set of first-order differential equations coupled with each other are simplified to 4 independent equations, leading to Bloch equations for dressed atoms through which all the coherent interactions of atoms with light can be extended to the case of dressed atoms.
In this paper comparisons of the two methods in settlement prediction is presented, and it is proved that their one order differential equation is strict consistent, which it is important for the application of Grey Model Theory in settlement prediction.
The chaotic motions of axial compressed nonlinear elastic beam subjected to transverse load were studied. Considering material and geometric nonlinearity, nonlinear partial differential equation of the system was derived. Under ideal displacement conditions,one order differential equations were devived and solved.
But PID controller only concerns error's one order differential only, does not concern the second and high order of error's differential, thus the PID controller can't depict dynamical behavior perfectly.
A new mathematical model of unsteady aerodynamics of airplane at high angles of attack is developed, with employment of a one order differential equation to describe the aerodynamic increment caused by nonlinear unsteady effects.
The thesis states the high order differentiator (HOD) that does not depend on the model of the controlled plant. The HOD can extract high quality one-order differential signal and high-order differential signals of the given signal.
本文论述了不依赖被控对象模型的高阶微分器(High order differentiator-HOD),该HOD能高品质的提取信号的一阶微分及高阶微分信号。
A Scalar wave equation with an aix direction variate z is used to describe a single-mode taper fiber, and the scalar wave equation is changed to one-order differential equations group by a Simple transform.
The governor dynamics equation was expressed by two one-order differential equations, and a continuous function - function sigmoid was used as a substitute of function sign. So the dynamics equation can be solved conveniently by applying numerical integral methods, and the oscillation of the result within a small range can be avoided.