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2009•Journal of Dalian UniversityRequires access

The Popularization of the Method of Constant Variation in Ordinary Differential Equation

Xuesheng Liu

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Abstract

The method of constant variation is an effective way to solve the first order non-homogeneous linear ordinary differential equation.This paper studies the first order ordinary differential equation in a special form,and proves that the equation of variable divided,Bernoulli equation,some non-homogeneous equations and the first order non-linear ordinary differential equation in another form can all be solved with this method,and then popularizes the method of constant variation.

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What this paper is about

The method of constant variation is an effective way to solve the first order non-homogeneous linear ordinary differential equation.This paper studies the first order ordinary differential equation in a special form,and proves that the equation of variable divided,Bernoulli equation,some non-homogeneous equations and the first order non-linear ordinary differential equation in another form can all be solved with this method,and then popularizes the method of constant variation.

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Available abstract

The method of constant variation is an effective way to solve the first order non-homogeneous linear ordinary differential equation.This paper studies the first order ordinary differential equation in a special form,and proves that the equation of variable divided,Bernoulli equation,some non-homogeneous equations and the first order non-linear ordinary differential equation in another form can all be solved with this method,and then popularizes the method of constant variation.

Key concepts: Homogeneous differential equation, Bernoulli differential equation, Mathematics, Ordinary differential equation, Exact differential equation, Variation of parameters, Riccati equation, Constant (computer programming)

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