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A New Solvable Type of Second Order Linear DifferentialEquation with Variable Coefficients

Zhang Xue-yuan

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Abstract

In this paper, a kind of linear differential equation with variable coefficients is turned into second order linear differential equation with constant coefficients through double transformation——linear and self-variable transformation of unknown function, then a new soluable, type of second order linear differential equation with variable coefficients is obtained. Thus, the famous second order Euler equation is expanded.

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What this paper is about

In this paper, a kind of linear differential equation with variable coefficients is turned into second order linear differential equation with constant coefficients through double transformation——linear and self-variable transformation of unknown function, then a new soluable, type of second order linear differential equation with variable coefficients is obtained. Thus, the famous second order Euler equation is expanded.

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Available abstract

In this paper, a kind of linear differential equation with variable coefficients is turned into second order linear differential equation with constant coefficients through double transformation——linear and self-variable transformation of unknown function, then a new soluable, type of second order linear differential equation with variable coefficients is obtained. Thus, the famous second order Euler equation is expanded.

Key concepts: Mathematics, Linear differential equation, Homogeneous differential equation, Variable (mathematics), Constant coefficients, Mathematical analysis, Constant (computer programming), Differential equation

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