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在微分方程式dy/dx=k_1 (y_∞-y)/x中,y与x分别为应变量和自变量,K_1为比例常数,y_x为y的渐近极限值。业已发现,在描述诸如速度过程等自然现象时,该方程式是很有用的。此微分方程的简化近似式为 dy/dx=k_2(y_(app)-y)及dy/dx=k_2(1-y)式中k_2是另一比例常数,y_(app)是y_∝的近似值。业已发现,此近似式在描述某些其他自然现象诸如过滤过程、粒度分布、矿粒破碎等方面也特别适用。关于用图解法求解y值以及这些方程式的数学特征,本文也用一些例子进行了讨论。
In the differential equation dy / dx = k_1 (y_∞-y) / x, y and x are the dependent variables and strain variables respectively, K_1 is the constant of proportionality, and y_x is the asymptotic limit value of y. It has been found that this equation is useful in describing natural phenomena such as velocity processes. A simplified approximation for this differential equation is dy / dx = k_2 (y_ (app) -y) and dy / dx = k_2 (1-y) where k_2 is another proportional constant and y_app is the approximation of y_α . It has been found that this approximation is also particularly useful in describing some other natural phenomena such as the filtration process, particle size distribution, ore particle breakup and the like. There are also some examples for the discussion of the y value solved graphically and the mathematical characteristics of these equations.