利用积分因子把非恰当微分方程转化为恰当微分方程是求解非恰当微分方程的重要手段。如何寻找合适的积分因子是转化问题关键之所在。首先,给出非恰当微分方程存在三种类型积分因子的充要条件。然后,给出相应的例子说明这些充要条件的应...利用积分因子把非恰当微分方程转化为恰当微分方程是求解非恰当微分方程的重要手段。如何寻找合适的积分因子是转化问题关键之所在。首先,给出非恰当微分方程存在三种类型积分因子的充要条件。然后,给出相应的例子说明这些充要条件的应用。最后,对这些充要条件进行简单总结并提出一些研究展望。It is an important means to solve non-exact differential equations by transforming them to exact differential equations using integral factors. How to find the appropriate integrating factors is the key to the transformation problem. Firstly, we present the sufficient and necessary conditions for the existence of three types of integral factors for non-exact differential equations. Then, some examples are given to illustrate the application of these necessary and sufficient conditions. Finally, these necessary and sufficient conditions are summarized briefly and some research prospects are put forward.展开更多
文摘利用积分因子把非恰当微分方程转化为恰当微分方程是求解非恰当微分方程的重要手段。如何寻找合适的积分因子是转化问题关键之所在。首先,给出非恰当微分方程存在三种类型积分因子的充要条件。然后,给出相应的例子说明这些充要条件的应用。最后,对这些充要条件进行简单总结并提出一些研究展望。It is an important means to solve non-exact differential equations by transforming them to exact differential equations using integral factors. How to find the appropriate integrating factors is the key to the transformation problem. Firstly, we present the sufficient and necessary conditions for the existence of three types of integral factors for non-exact differential equations. Then, some examples are given to illustrate the application of these necessary and sufficient conditions. Finally, these necessary and sufficient conditions are summarized briefly and some research prospects are put forward.
