论文部分内容阅读
1问题背景由于非线性微分方程求解是一个复杂的问题,一般教材内容涉及也不多。本文将讨论以下二阶微分方程的解。y″+(axx+b)y′+(cx+d)y=0(a≠0,c≠0)。①由于线性微分方程的解法,是通过待求解形式:y=e~(λx)(λ为待定系数),将线性微分方程化为代数方程求解~([1])。因此,本文也将利用代数方程,讨论方程①形如y=e~(λx)(λ为待定系数)的解。2理论讨论在微分方程①中,令y=e~(λx)(λ为待定系数),带入
1 Problem Background Since the solution of nonlinear differential equations is a complex issue, the content of general textbooks does not involve much. This article will discuss the solution of the following second-order differential equations. y′′+(axx+b)y′+(cx+d)y=0 (a≠0, c≠0).1 Since the solution of the linear differential equation is through the form to be solved: y=e~(λx) (λ is the undetermined coefficient), the linear differential equation is transformed into algebraic equation solution ~ ([1]). Therefore, this paper will also use algebraic equations to discuss equation 1 as y=e~(λx) (λ is the undetermined coefficient) (2) Theoretical discussion In the differential equation 1, let y=e~(λx) (λ is the undetermined coefficient) and bring it into