 # 浙江大学竺可桢学院保持共产党员先进性教育活动

The solution of ordinary differential equations

Abstract: This paper mainly discusses some related solutions of the first-order and higher-order ordinary differential equations． This paper firstly introduces the basic concept of differential equations． on such a basis, the paper probes into the solutions of the first-order differential equations including the main types such as variable separable equation, separable variable equations which can be translated into the equation homogeneous equation, a linear differential equations and the proper equation． To solve such types of first-order differential equation, the methods can be used: variable separation, transformation, a linear equation of constant change of law and the appropriate equations direct observation, portfolio breakdown, integral contrast． Finally，it discusses the solutions of the higher-order differential equation． The solution are non-homogeneous linear equation of constant variation , Euler be determined index of constant coefficient of linear equations, nonhomogeneous linear equations comparison method and Laplace transform method． In addition, the method of transform is used to solve two special second ordinary differential equations．

Keywords: first-order ordinary differential equations; higher-order ordinary differential equations; Solution ．