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2009•Journal of Huzhou Teachers CollegeRequires access

Equation of Homogeneous Type and Its Solution

Gao Jin-qing

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Abstract

This paper studies the equation of a homogeneous type,which is the generalized form of homogenous equation in the first order differential equation.The procedure of solving the homogenous differential equation by a variable transformation method is generalized to solve equations of the homogenous type.Meanwhile,the author proves that the equation of a homogenous type is an integrable equation and gets some new integrable differential equations of the first order,including Reccati equation and Bernoulli equation.

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What this paper is about

This paper studies the equation of a homogeneous type,which is the generalized form of homogenous equation in the first order differential equation.The procedure of solving the homogenous differential equation by a variable transformation method is generalized to solve equations of the homogenous type.Meanwhile,the author proves that the equation of a homogenous type is an integrable equation and gets some new integrable differential equations of the first order,including Reccati equation and Bernoulli equation.

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Available abstract

This paper studies the equation of a homogeneous type,which is the generalized form of homogenous equation in the first order differential equation.The procedure of solving the homogenous differential equation by a variable transformation method is generalized to solve equations of the homogenous type.Meanwhile,the author proves that the equation of a homogenous type is an integrable equation and gets some new integrable differential equations of the first order,including Reccati equation and Bernoulli equation.

Key concepts: Bernoulli differential equation, Homogeneous differential equation, Differential equation, First-order partial differential equation, Mathematics, Exact differential equation, Integrable system, Riccati equation

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