基于弹性升阶变换法的一类可化为合流超几何方程的一阶非线性常微分方程的求解
Solving a Class of First-Order Nonlinear Ordinary Differential Equations Which Can Be Transformed into Confluent Hypergeometric Equation Based on Elastic Upgrading Transformation Method
摘要: 根据弹性的可分析一个变量对另一个变量的相对变化率的特性，本文创新性的引进了一种微分变换——弹性升阶变换，用于解决一类一阶非线性常微分方程的求解问题；它可将一阶非线性常微分方程转化为合流超几何方程，从而求得其解；并归纳总结出可扩展应用该方法的解题步骤。该方法为某些一阶非线性常微分方程的求解提供了一种新方法，从而扩大了微分方程的可解类。
Abstract: According to the characteristic of elasticity that can analyze the relative rate of change of one var-iable to another, this paper innovatively introduces a differential transformation, the elastic up-grading transformation, for solving a class of first-order nonlinear ordinary differential equations. It can transform the first-order nonlinear ordinary differential equation into a confluent hypergeometric equation, and thus find its solution, and summarize the steps of applying the method to solve the problems. This method provides a new method for solving some first-order nonlinear ordinary differential equations, so that the solvable type of differential equations is expanded.
文章引用：付雪倩, 李顺初, 刘盼, 邵东凤, 范林. 基于弹性升阶变换法的一类可化为合流超几何方程的一阶非线性常微分方程的求解[J]. 理论数学, 2023, 13(5): 1227-1233. https://doi.org/10.12677/PM.2023.135126

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