摘要
利用恰当微分方程和积分因子的定义,讨论了一类乘积型积分因子的存在性条件,得到了方程在此定理条件下的通解公式,并结合实例给出求解此类型积分因子的具体方法,进一步利用通解公式得到方程通解.
By using the definitions of the exact differential equations and integral factors,the existence conditions of a class of product integral factors are discussed,and the general solutions of the equations under the condition of this theorem are obtained.The concrete methods for solving the integral factors of this type are given with an example,and the general solution of the equation is obtained by using the general solution formula.
引文
[1]王高雄,周之铭,朱思铭,等.常微分方程[M].北京:高等教育出版社,2006.
[2]陈星海,李璜,韩祥临.三类复合型积分因子的充分必要条件及其应用[J].湖州师范学院学报,2010,32(2):44-49.
[3]张海燕,戴扬,陈洁.新复合型积分因子的存在定理及应用[J].皖西学院学报,2007,23(2):7-9.
[4]王景艳,杨玲.一类特殊积分因子存在的充要条件及其应用[J].高等数学研究,2015,18(3):29-30.
[5]郭三刚.全微分方程与积分因子定义的修正[J].高等数学研究,2018,21(3):7-9.