基于弹性升阶变换求解一类可化第一种Weber方程的微分方程初值问题

Elastic Ascending Order Transformation Method for Solving the Initial Value Problem of a Class of Differential Equation Transformed into the First Weber Equation

对于非线性常微分方程初值问题的求解,并没有一般化的求解方法,于是根据弹性的特性引入了一种新的微分变换-弹性升阶变换.针对一类一阶非线性常微分方程的初值问题,通过弹性升阶变换,把它转化成第一种Weber方程的初值问题,从而获得其解.弹性升阶变换的应用不仅扩大了微分方程的可解类,而且为微分方程初值问题的求解提供了新思路.

There is no general solution to the initial value problem of nonlinear ordinary differential equations.Therefore,this paper introduces a new differential transformation-elastic ascending transformation according to the characteristics of elasticity.For the initial value problem of a class of first-order nonlinear ordinary differential equations,the solution can be obtained by transforming it into the initial value problem of the first Weber equation through the elastic ascending transformation.The application of elastic ascending transformation not only expands the solvable class of differential equations,but also provides new ideas for solving the initial value problems of differential equations.