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2003•Journal of Shanghai Second Polytechnic UniversityRequires access

A New Solvable Type of Second Order Non-Linear Differential Equation

Xueyan Zhang

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Abstract

In this paper, a new type of second order non-linear differential equation is first led from physics example, and then the concept of characteristic equation is led into it, then it is proved to that this kind of non-linear differential equation is solvable with the methods of the transformation of unknown function, the transformation of independent, and elementary algebraic. The characteristic root expression formula of its general solution was given, thus the solvable range of ordinary differential equation was extended.

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What this paper is about

In this paper, a new type of second order non-linear differential equation is first led from physics example, and then the concept of characteristic equation is led into it, then it is proved to that this kind of non-linear differential equation is solvable with the methods of the transformation of unknown function, the transformation of independent, and elementary algebraic. The characteristic root expression formula of its general solution was given, thus the solvable range of ordinary differential equation was extended.

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Available abstract

In this paper, a new type of second order non-linear differential equation is first led from physics example, and then the concept of characteristic equation is led into it, then it is proved to that this kind of non-linear differential equation is solvable with the methods of the transformation of unknown function, the transformation of independent, and elementary algebraic. The characteristic root expression formula of its general solution was given, thus the solvable range of ordinary differential equation was extended.

Key concepts: Mathematics, Universal differential equation, Exact differential equation, Homogeneous differential equation, First-order partial differential equation, Linear differential equation, Algebraic differential equation, Characteristic equation

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